Papers

Ultrashort laser pulses can induce order out of chaos. A femtosecond pulse melts a metal surface for about a hundred picoseconds; under photoexcitation with no net polarization axis, the resolidifying film nonetheless organizes into regular nanoscale patterns. Here we derive from first principles the nonlinear hydrodynamics responsible for it and show it accounts for the full phase diagram of morphologies from measurable laser and material parameters. Starting from the Navier-Stokes equations in the lubrication limit, the molten film obeys a damped Kuramoto-Sivashinsky equation that reduces to a Swift-Hohenberg formalism near threshold, with every coefficient fixed by the laser fluence, melt thickness, optical skin depth, and thermocapillary response. The ratio of melt depth to optical skin depth sets the pattern wavelength, while the inter-pulse delay, via post-pulse damping, gates the route from flat surface to ordered pattern to chaos. We validate the phase diagram (hexagonal cavity arrays, bistable mixed states, labyrinths) numerically and confront it with pulse-resolved experiments on two metals, Ni and Fe3Cr. The agreement between theory and experiment quantitatively links the microscopic laser-material response to the macroscopic pattern selected after many pulses. This order is self-limiting: the same corrugation the instability builds scatters the modes that build it, and simulations, with every scale fixed by material parameters, place the coherence breakdown near a roughness of 30 nm after a few tens of pulses, a finite window confirmed by pulse-by-pulse measurements of orientational order on the experimental surfaces; at stronger coupling, disorder does not destroy the pattern but saturates and pins it instead. This yields a closed, predictive description of laser-driven self-organization, from single-pulse melt dynamics to the arrest of nanoscale order.

In this work, we construct analytical kink-antikink $(K\bar{K})$ configurations in the non-integrable $\varphi^4$ model by mapping exact solutions of the integrable sine-Gordon system via a field deformation. This procedure yields two distinct classes of configurations, parametrized by the initial half-separation and velocity. We compare these profiles with the standard additive superposition Ansatz in terms of vacuum structure and equation-of-motion residuals, deriving explicit closed-form expressions for the corresponding integrated squared residuals. For small separations, the mapped soliton-antisoliton configurations exhibit appreciably smaller residuals than the naive superposition Ansatz, which in turn performs better than the mapped two-soliton configurations. Although the mapped fields are not exact solutions of the $\varphi^4$ equation of motion, they provide mathematically consistent, topologically sound, and physically motivated initial data for numerical studies of kink-antikink scattering and resonance phenomena.

We observe the emergence of extreme events in an active fluid involving two distinct chemical species that regulate active stress. One species is slow diffusing and the other is fast diffusing, and the growth of the fast-diffusing species is modelled using a nonlinear logistic term. We demonstrate the presence of extreme events in the temporal evolution of the concentrations, as well as in the spatial profile of the system,in regimes of merging-emerging soliton-like dynamics and spatio-temporal chaos, through analysis of the time-series, bifurcation diagrams, probability distribution functions of the concentration of the two species, return maps and distributions of inter-event intervals. Interestingly, we also find evidence of pronounced bunching of extreme events and super-extreme events in the slow chemical species in the soliton-like regime. We go on to systematically explore the dependence of the extreme event occurrences on the Péclet number and the strength of the nonlinear growth term, and find that the probability of extreme events increases after a critical Péclet number, while increasing the nonlinearity suppresses extreme events. Lastly, in order to gain further insight, we investigate a modified mode-truncated reduced order model comprising of coupled differential equations mimicking this active fluid system. We find that this reduced order model also exhibits extreme events whose emergence is correlated with a sudden expansion in attractor size due to a crisis arising from attractor collision.So these results demonstrate the existence of extreme events in an active fluid system, and are of potential relevance to biological phenomena where active transport plays an important role.

I consider vortex solitons in two-dimensional star networks created by several one-dimensional line waveguide arrays (or rays) brought in close proximity. First waveguide in each array belongs to the ring of certain radius and its modal field overlaps with modal fields of waveguides from other rays laying on this ring, as well as with modal fields of waveguides in this line array. This creates a system with discrete rotational symmetry that is capable of supporting various localized linear vortex states due to local coupling between waveguides on the central ring, where line arrays approach each other. Localized vortex states emerge from the continuum of the states extended along the rays of the structure upon variation of the radius of the central ring. I show how different vortex modes with progressively increasing topological charges emerge when the number of rays in structure and, therefore, its discrete rotational symmetry increases. Each such linear localized mode gives rise to a family of thresholdless vortex solitons in nonlinear optical medium, whose topological charges are limited by the discrete rotational symmetry of the system. Vortex solitons in star networks exhibit qualitatively different behavior with increasing power depending on whether the propagation constant of linear vortex that gives rise to a family of solitons is located above or below the band of extended states. Stability properties of vortex solitons nontrivially depend on their topological charge and discrete rotational symmetry of the system, showing very different picture from usual ring-like waveguide arrays.

For a model of a thin spherical layer of an incompressible rotating fluid subjected to the action of Coriolis and buoyancy forces, both analytical solutions in the form of stationary thermal spots moving along the equator and self-similar solutions are found. The influence of the parameters determining the shape of the spots on their propagation speed and direction is studied. It is found that the speed and direction of motion of the spots depend not only on the sign of their thermal contrast with the background flow, but also on the ratio of the semi-axes determining their shape. In particular, if the ratio of the equatorial semi-axis to the meridional one $b/a$ is equal to $\pi/2$, the spots are at rest. If the spots are elongated along the equatorial axis to such an extent that $b/a>\pi/2$, then “cold” spots move westward and “hot” spots move eastward. Under the condition $0.747\leq b/a<\pi/2$, the situation is reversed: “hot” spots move westward and “cold” spots move eastward. Self-similar solutions in the model are realized strictly in the form of circular thermal spots, and their radius varies according to a power law with a scaling exponent $k$, which is determined by the behavior of the cross-frontal buoyancy gradient on the spot contour. We note that the regime $k=1/4$ is realized under the assumption of a constant buoyancy gradient, while the regime $k=1/6$ corresponds to the conservation of total buoyancy.

We present an extended study of the gravitationally localized soliton-like solutions to the minimally-coupled Einstein-Dirac-Higgs equations, embedded in asymptotically Minkowski spacetimes. The equations of motion describing these Yukawa-coupled Dirac stars are generalized to any even number of constituent fermions. We first expand the discussion of two-fermion ground-state solutions initially analyzed in Leith et al. [Phys. Rev. D. 107, 106020 (2023)]. Upon extending our analysis to excited states and many-fermion states, we find that both exhibit different behaviors to their two-fermion ground-state counterparts. In these excited states and many-fermion states, the Higgs field may exhibit stepwise increases and at times decrease within the soliton, which has not been seen for the two-fermion ground states. We also propose the potential cause of a significant degree of ADM-to-fermion mass disparity, which is present in states with strong Yukawa-coupling.

We prove the existence of two kinds of self-similar vector solitons in an inhomogeneous optical fiber medium, where light propagation is governed by a pair of coupled higher-order nonlinear Schrodinger equations with varying second- and third-order dispersions, self- and cross-phase modulation non linearities, self-steepening, and linear gain/loss effects. The newly found self-similar waves comprise bright-W-shaped and kink-antikink waveforms with nonvanishing amplitudes. As a practical exam ple, we discuss the propagation dynamics of these soliton structures in a periodically distributed fiber system as well as an exponential dispersion-decreasing fiber. The results demonstrate that the parameter functions of gain/loss and third-order dispersion serve as a key factor in determining the nonlinear dynamics of self-similar vector solitons. In particular, we find that precise control over the shape and dynamic evolution of self-similar pulses can be achieved through a proper choice of the distributed third-order dispersion parameter, while the gain/loss coefficient controls their intensity.

The characteristic intersection angle of the desiccation crack relaxes from near \ang{90} toward \ang{120} under repeated drying–wetting cycles. However, the theoretical understanding of this relaxation is insufficient, especially the modeling of the drying–wetting cycles. Here we introduce a phase-field model of desiccation fracture, extending the model proposed in previous studies by adding crack healing and a scar effect left by past cracks. By repeating drying–wetting cycles in a finite element simulation, we find that the angle distribution develops a growing peak near \ang{120} as the cycle number increases, consistent with experiments. The standard deviation of the intersection angle from \ang{120} relaxes exponentially with a characteristic time of about 2.85 cycles. These results are consistent with experiments, except that the characteristic time is slightly smaller than the experimental value. Crack energy dominates the total energy and also relaxes exponentially with nearly the same characteristic cycle as the angle relaxation. This decay is driven mainly by a shortening of the effective crack length rather than a change in effective fracture toughness.

Internal waves often propagate in the presence of currents. Internal waves and currents are widespread in the world's oceans. The equatorial internal waves and the equatorial undercurrent (EUC) are perhaps the most representative illustration of this phenomenon. The current profile in this study is a quadratic function of depth, which is in agreement with the known results of the EUC. With this assumption the integrable nonlinear Gardner's equation is derived as a model for the wave motion of the thermocline, separating the two layers of slightly different densities. In addition, we derive the generalised Gardner's equation in the case of variable bottom. We demonstrate that the coefficients of the equation are very sensitive with respect to the parameters of the EUC.

Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of $10^3$ to $10^5$ while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.

Vortex light fields carry orbital angular momentum and have attracted significant attention because of their wide applications in light field manipulations, optical communications, and quantum information processing. In nonlinear media, the balance between diffraction and self-action enables the formation of vortex solitons. However, achieving the stability of vortex solitons remains challenging due to radial and azimuthal modulation instabilities. Here, we report stable vortex solitons and vortex-soliton arrays in disclination-fractal configurations with different rotational symmetries, constructed by applying disclination operations to fractal lattice structures. The stable vortex-soliton arrays—composed of several vortex solitons—can exist along domain walls, resulting from the disclination operation applied to the topologically trivial phase. Their stability is verified through both linear stability analysis and direct simulations of perturbed propagation. For comparison, vortex-soliton arrays in conventional disclination configurations are found to be completely unstable, demonstrating the significance of the fractal configuration in stabilizing these nonlinear states. These findings reveal a new nonlinear excitation mechanism arising from the interplay between fractal geometry and disclination defects, thereby providing theoretical underpinnings for both the improved understanding of multi-field excitation phenomena in complex geometric systems and opening new avenues for the design of photonic devices based on fractal disclination structures.

Nonlinear wave equations exhibit rich interplay among dispersion, nonlinearity, coupling, dissipation, and external forcing, producing diverse coherent and complex wave structures. Although exact travelling-wave solutions provide analytical benchmarks, their construction alone does not reveal underlying phase-space, bifurcations, stability, or responses to perturbations. This review presents a reduction-based methodological framework connecting nonlinear partial differential equations(PDEs) to reduced dynamical systems, invariant phase-space structures, exact waveform reconstruction, stability analysis, and verification in PDEs. Its applicability and limitations are examined across Schrödinger-type, coupled, nonparaxial, dissipative, magnetic, shallow-water, and fractional wave equations. Particular emphasis is placed on correspondence between analytical waveforms and invariant orbits. Equilibria, periodic trajectories, homoclinic orbits, and heteroclinic connections geometrically represent constant, periodic, localized, and front-like structures, respectively. This review distinguishes existence and stability of invariant structures from onset of chaos, emphasizing complementary diagnostics rather than reliance on phase-portraits or finite-time indicators alone. Major methodological gaps include incomplete parameter-space characterization, weak correspondence between reduced models and full-PDE dynamics, ambiguities in generalized and fractional formulations, limited robustness analysis, inadequate numerical reproducibility, and insufficient links to experimental observables. The framework prioritizes physical admissibility, stability, robustness, and predictive relevance over generation of additional formal solutions. It supports reliable nonlinear wave prediction, stability assessment, control, and system design in fluid, optical, plasma, and other nonlinear physical systems.

We consider a minimal pressure-based model of heterogeneous cell populations consisting of proliferative and non-proliferative cells with different mobilities. The model is formulated as a system of reaction–cross–diffusion equations describing the spatio-temporal dynamics of the cell densities. The model is known to admit one-dimensional travelling wave solutions with strictly segregated components: non-proliferative cells occupy a finite region at the leading edge, while proliferative cells remain at the rear. However, the speed, parameter dependence, and stability of these waves remain poorly understood. In this work, we derive an almost explicit variational bound on the wave speed by reformulating the problem as a free-boundary problem for a generalised porous–Fisher equation. The estimates we obtain apply to general pressure laws and growth kinetics, agree closely with the results of numerical simulations, and become sharp in the incompressible limit, where we formally recover a fully explicit characterisation of the wave speed. We then analyse the stability of the waves to show that segregated waves are stable only when non-proliferative cells are more mobile than proliferative cells. Finally, motivated by numerical observations of finger-like protrusions, we investigate the stability of incompressible segregated circular waves through asymptotic shape-perturbation analysis. This yields explicit expressions for the pressure, interface velocity, and growth rates of angular modes, thereby making evident the destabilisation mechanisms that may lead to the emergence of fingering instability. Interestingly, we find that, in contrast with the one-dimensional case, the stability of such circular waves is not determined solely by the relative value of the mobility coefficients, and thus instabilities may arise irrespective of which cell type has the larger mobility.

We consider Thouless pumping of two-dimensional quadratic solitons composed from coherently interacting fundamental frequency (FF) and second harmonic (SH) components propagating in a periodic $\chi^{(2)}$ material. The pumping is induced by two mutually sliding two-dimensional lattices defined by shallow transverse and longitudinal periodic refractive index modulation. Focusing on solitons in the semi-infinite gap, we find three distinct pumping scenarios: the absence of transport for small-amplitude solitons, non-quantized transport in a transient regime at intermediate amplitudes, and stable quantized transport for solitons with relatively large amplitudes. Different directions of the sliding velocity were investigated resulting in different trajectories of soliton center. The transition to the regime of quantized transport is found to depend strongly on phase mismatch between FF and SH waves that also influences stability properties of two-dimensional $\chi^{(2)}$ lattice solitons. We also show that pumping with longitudinal periods in the x and y directions, whose ratio approximates an irrational number, induces quantized transport whose direction rapidly converges, with increase of the accuracy of the approximation, to a limiting pumping direction determined by this irrational number and corresponding to truly incommensurate longitudinal periods.

Recently, a soliton mechanism for room-temperature superfluorescence in thin perovskite films has been proposed, with a fundamental soliton predicted to remain stable under LO phonon–exciton interactions. At the same time, superlattice architectures offer a route to enhancing superfluorescence in perovskites. Motivated by recent observations of room-temperature superfluorescence in periodic superlattices of quasi-2D metal-halide perovskites, we extend the 2D nonlocal nonlinear Schrödinger equation describing Wannier exciton–LO phonon interactions to superlattice structures, obtaining a 3D nonlocal nonlinear Schrödinger equation. We show that interlayer tunnelling gives rise to breather dynamics corresponding to a stable fundamental soliton in mixed coordinate–momentum space, with the coordinate parallel to the layers and the momentum perpendicular to them. The breather dynamics originate from miniband formation, which induces a momentum-dependent phase modulation of the soliton. In the absence of interlayer tunnelling, the breather dynamics disappear and the soliton becomes stationary. These results establish a direct connection between interlayer tunnelling, miniband formation and soliton dynamics, suggesting that breather behavior can provide a signature of interlayer tunnelling in quasi-2D perovskite superlattices.

Quantized vortices are ubiquitous in physics, spanning superconductivity, astrophysics, superfluid condensed matter systems, and nonlinear optics. Yet embedding vorticity into topologically protected nonlinear states has remained a major challenge, with all previously observed corner solitons in higher-order topological insulators (HOTIs) exhibiting only trivial phase distributions. Here, we report on the first realization of stable topological corner vortex solitons in a photonic fractal HOTI. Using an array of laser-written waveguides in the shape of Sierpiński gasket with a controllable distortion, we design linear topological vortex modes, from which nonlinear corner vortex solitons bifurcate. Moreover, we demonstrate that these solitons exhibit exceptional robustness across a broad power range and, unlike vortex solitons in topologically trivial lattices, form without a power threshold. Our results introduce the angular momentum degree of freedom into the physics of topological corner modes, opening prospects for topologically protected vortex-based photonics.

The ability to precisely shape the properties of light over multiple degrees of freedom constitutes the foundation of modern photonic architectures. Broadband sources with addressable spectro-temporal content are for instance critical for applications spanning biomedical imaging, material processing, lidar, and ultrafast spectroscopy, but also key enabling technologies in quantum information processing, high-capacity communications, and optical computing. Yet, flexible and adjustable spectro-temporal shaping so far remains a significant challenge, as it requires the simultaneous manipulation of both frequency and temporal domains across broad spectral bandwidths and extended timescales, from femtoseconds to nanoseconds. Importantly, conventional approaches to spectro-temporal processing typically rely on bulky and complex optical systems that lack scalability and flexibility, ultimately hampering their utility for applications requiring addressable multiphotonic processes. Here, we present a framework for spectro-temporal wavepacket control over a broad bandwidth, merging programmable integrated photonics with high-speed optical characterization. Leveraging machine leaning for tailoring nonlinear pulse propagation, we experimentally report scalable and on-demand shaping of broadband ultrafast pulse patterns. We demonstrate the efficacy of our method through reconfigurable power across 400 nm bandwidth with picosecond resolution, with promises for applications where precise control over light is paramount, in particular those needing versatile and controllable multiphoton excitations.

We investigate novel vector localized wave solutions in the coupled Lakshmanan-Porsezian-Daniel equa?tions, which describe the dynamics of the Heisenberg ferromagnetic spin chain. We present Tajiri-Watanabe breathers, rogue waves and resonant modes in both the degenerate and non-degenerate regions, together with the degenerate beating solitons. The fourth-order effect induces state transitions in both regions. In particular, the degenerate breathers can be transformed into solitons, whereas such transitions are absent in the coupled Hirota equations. Moreover, beating solitons can be converted into stable solitons only in the degenerate region, the phenomena not found in the Manakov system. We further uncover the state transitions of the resonant modes and derive the corresponding transition conditions for each branch. We derive the physical spectra and subsequently identify the state transition conditions in the spectral domain for both the degenerate and non-degenerate cases. These spectra provide an additional characterization of the transition dynamics. Finally, direct numerical simulations are performed to verify the validity of the exact solutions.

Condensates can accelerate reactions by concentrating reactants, yet product accumulation can eliminate this advantage. We show that product-induced suppression of condensation generates rotating, deforming, and propagating condensate domains through spontaneous symmetry breaking. Their reorganization shifts reaction sites away from accumulated products while retaining reactant enrichment, yielding rates above those of static condensates and homogeneous states. Reaction flows can thus self-organize condensates into dynamic reactors, with implications for biological and synthetic systems.

Programmable control of individual pulses in a high-repetition-rate (typically MHz) ultrafast pulse train is a long-standing goal for optical arbitrary waveform synthesis. Here, we report a programmable pulse-by-pulse shaper that enables deterministic spectral-temporal control of ultrafast pulses at a repetition rate of $\sim$ 20~MHz. By synchronizing an FPGA-driven electro-optic modulation on the stretched waveform in a temporal 4$f$ shaping system, the regime writes pulse-index-dependent spectral phase profiles onto individual pulses. We demonstrate three levels of programmable ability: zero-order phase coding that maps pulse-by-pulse phase sequences into double-slit-like spectral-temporal interference; first-order phase programming that produces arbitrary temporal trajectories with deterministic delay; and fractional-order phase engineering that generates programmable temporal breathing. By launching the shaped pulse train into a nonlinear fiber stage, the programmed temporal breathing is converted into one spectral breathing. We further construct a phase-level-dependent regime map of nonlinear spectral breathing, revealing transitions from weak single-envelope breathing to multi-peak spectral splitting and strongly breathing merged-spectrum dynamics, in agreement with numerical simulations. This pulse-by-pulse spectral-temporal synthesis platform establishes pulse index as a programmable degree of freedom for ultrafast pulse shaping and provides a route toward real-time and pulse resolved optical arbitary waveform synthesis.

We investigate shortcut-to-adiabaticity protocols for the rapid compression of optical solitons in nonlocal media. Using a variational approximation, we derive an effective Ermakov-like equation for the soliton width and employ inverse engineering to design propagation-dependent control parameters. Three control strategies are compared, based respectively on modulation of the characteristic nonlocal length, the Kerr nonlinearity, and the external parabolic confinement. We show that all three protocols enable high-fidelity compression over strongly reduced propagation distances. By comparing control smoothness and final fidelity, we find that the relative performance of the protocols in the very short-distance regime depends on the chosen criterion, revealing a trade-off between implementation smoothness and target-profile accuracy. These results establish a practical and general route to fast soliton manipulation in nonlocal media.

We analyze an inverse problem for determining the piston speed and the associated flow field from a prescribed leading shock and the initial data in a shock tube. The gas flow is described by the isentropic Euler equations (i.e., the $p$-system), while the trajectory of the leading shock is prescribed as a given Lipschitz curve. Under an Oleĭnik-type entropy condition on the leading shock, we develop a modified wavefront tracking scheme to construct the flow field behind the shock. This construction enables us to determine the corresponding piston speed and the associated flow field.

Solutions of the Whitham modulation equations for one-phase periodic waves obeying the sine-Gordon equation are found that describe the evolution of an oscillatory region behind an instability front propagating into the instability region. A simple self-similar solution describes the whole region between two fronts of instability resulting from a localized initial disturbance in the unstable state. Another hodograph solution represents typical waves close to the instability fronts. This theory generalizes the approach used previously for systems obeying the nonlinear Schroedinger equation.

We report the measurement of the critical velocity of a paraxial superfluid of light flowing past a mobile impurity, realized using a dual-wavelength optical scheme in a warm vapor of $^{87}\text{Rb}$. The superflow is two-dimensional by nature, while the impurity features a highly repulsive potential, a large tunable radius, and a finite mass. The critical velocity is evaluated by simultaneously monitoring three complementary observables: the number of vortices nucleated in the wake of the impurity, the hydrodynamic force exerted on it, and its displacement velocity relative to the flow. These independent methods yield consistent values for the critical velocity, which remain systematically below the Landau criterion and decrease with the impurity radius, in qualitative agreement with theoretical expectations. Our results demonstrate the reliability of these combined diagnostics, establishing paraxial superfluids of light as a versatile platform for exploring the impurity problem in quantum hydrodynamics.

The propagation of narrowband wave packets is a classical problem with broad relevance across nonlinear wave physics. Within the framework of the nonlinear Schrödinger equation, solitons are known to propagate without changing shape, whereas Gaussian envelopes may undergo substantial reshaping depending on the balance between dispersion and nonlinearity. Here, we combine laboratory experiments with numerical simulations to systematically investigate the evolution of hydrodynamic Gaussian wave packets over a wide range of amplitudes and spectral bandwidths. We show that when the envelope amplitude and width match those of the stationary NLSE soliton solution, the wave packet propagates steadily in the wave flume. More generally, by varying the amplitude of the Gaussian envelope, the wave packet may undergo either dispersive broadening or nonlinear focusing, resembling the dynamics of Satsuma-Yajima breathers. These findings may facilitate the controlled generation and manipulation of localized wave packets in a variety of nonlinear dispersive systems, including optics, plasmas, and Bose-Einstein condensates.

Being structures characterized by discrete rotational symmetry $\mathcal{C}_\nu$ of order $\nu$, photonic quasicrystals are capable to support stable propagation of linear vortex-carrying light beams and vortex solitons. However, the impact of discrete rotational symmetry $\nu$ of quasicrystals on the properties of vortex light states was not investigated so far, as only the systems constructed using the simplest Penrose tiling or corresponding optically induced Penrose lattices were considered in this context. Here we propose a broad class of quasicrystals with global topological defects – disclinations – introduced into their structure that allows to produce new quasicrystalline structures with any desired order of discrete rotational symmetry from basic Penrose structure. Such global topological deformation substantially enriches linear spectrum of quasicrystals, allowing them to support new types of linear vortex states and bifurcating from them families of stable thresholdless vortex solitons with unusual intensity and phase distributions. We found two different classes of stable vortex solitons consisting of in-phase or out-of-phase pairs of closely located bright spots, with total intensity distribution reflecting particular discrete rotational symmetry of the quasicrystal with disclination. Remarkably, even low-charge vortex solitons can be stable in quasicrystals with disclinations, while stability intervals for them broaden with decrease of the discrete rotational symmetry $\mathcal{C}_\nu$ of quasicrystal. Our results expand the theory of localization in quasicrystals to structures with global topological deformation, highlighting new prospects for robust transmission of power or information arising in these systems.

The chaotic dynamics of a large one-dimensional lattice of nonlinear maps with a spatial coupling of increasing extent is explored using the covariant Lyapunov vectors (CLVs). A theoretical approach is developed that predicts the spectral variation of the CLVs and the spectrum of Lyapunov exponents. The theoretical approach is independent of the details of the mapping function and requires only a description of the lattice coupling. The general structure of the spatial power spectrum of the CLVs is determined using only the eigenvectors of the coupling matrix. This yields a decomposition of the CLVs into two regimes. The first regime, corresponding to the largest Lyapunov exponents, contains highly entangled CLVs with significant contributions from large scale spatial structures and aligns with the sorted eigenvectors, which occur in pairs with wavenumbers that increase linearly with their index. The second regime contains significant mixing of length scales with increasing index. The index separating these two regimes is approximately equal to the fractal dimension of the dynamics.

Continuous cellular automata such as Lenia spontaneously produce lifelike, self-propelling patterns, including the Orbium glider, which travels in a straight line while pulsing through a fixed breathing cycle. Collision-based logic, where moving patterns compute by colliding, is established in discrete cellular automata and continuous physical media. Within continuous cellular automata, computation has so far been trained into the rule rather than emerging from collisions, and whether a fixed-rule automaton like Lenia can support general collision-based computation remains open. This paper constructs an INHIBIT gate from collisions of the Orbium glider. Of the patterns searched across four continuous-CA rule types, the Orbium glider is the only one shown to survive a collision with both copies intact. A control glider deflects a signal glider off its output line, so the output carries a signal only when no control is present. The gate blocks across all twenty-four phases of the breathing cycle and nine integer offsets of the control. Two such gates in series, with one signal line and two controls, compose into an AND-NOT chain, correct on all eight input combinations. By contrast, routing a signal beyond that single chain is undemonstrated. A deflected signal is not restored to a fixed landing position, and no reusable absorber for the surviving gliders was found. The immediate open question for collision-based computation in Lenia therefore narrows from whether a gate exists to whether a deflected signal can be delivered to a downstream gate, the next requirement for composing the gate beyond a single straight chain.

We study linear instabilities and pattern formation in a spatially extended Selkov model for glycolysis with diffusion and chemotactic interactions between two species. Linear stability analysis reveals two distinct bifurcations: a zero-wavevector, finite-frequency Hopf bifurcation leading to spatially homogeneous oscillations, and a finite-wavevector Turing instability with a saddle-node bifurcation leading to stationary inhomogeneous patterns. The selected wavevector, $k_c$, depends sensitively on the nature and strength of chemotaxis and varies nonmonotonically with the chemotaxis parameters, allowing re-entrant transitions between homogeneous and patterned states. For sufficiently strong chemotaxis, when the two species mutually attract or mutually repel each other, an unusual instability emerges in which the preferred wavevector diverges as a finite threshold in chemotactic strength is approached. We complement the linear analysis with extensive direct numerical simulations (DNS) of the nonlinear partial differential equations in two dimensions. The DNS confirm the predicted instabilities and their nonmonotonic and re-entrant character, and also reveal spatially uniform oscillatory states for suitable parameters. The stationary patterns include spots and, unexpectedly, stable stripes. We further uncover transitions between spot and stripe morphologies controlled by chemotactic strength and diffusivity ratios. The stability of the striped states is consistent with linear amplitude equations, whereas the spot-stripe transition is attributed to nonlinear effects beyond linear stability. Our results demonstrate that chemotaxis can act as a nonmonotonic control parameter for instability selection, wavelength selection, re-entrant pattern formation, and nonlinear pattern morphology in reaction-diffusion systems.

We address the existence and dynamics of solitons propagating along helical (spiral-rotating) and straight trajectories in the bulk waveguide with the cubic-quintic nonlinearity and a single- or multi-ring potential. The input is taken as a vortex beam with a single or multiple phase singularities (pivots), displaced from the waveguide's axis. The single off-axis pivot creates a one-ring helical soliton, with a closed or open (split) ring structure. The vortex beams with multiple off-center pivots give rise to complex states with multi-ring, multi-core, and/or multi-split structures. The multi-core/split solitons propagate along helical channels, or straight ones, which are parallel to the propagation axis. The sign and period of the helicity can be precisely adjusted by applying a torque with an appropriate angular velocity.