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On general rogue waves in the parity-time-symmetric nonlinear Schrodinger equationMar 14 2019This article addresses the question of general rogue-wave solutions in the nonlocal parity-time-symmetric nonlinear Schrodinger equation. By generalizing the previous bilinear Kadomtsev-Petviashvili reduction method, large classes of rogue waves are derived ... More

Harmonic Stability of Standing Water WavesMar 13 2019A numerical method is developed to study the stability of standing water waves and other time-periodic solutions of the free-surface Euler equations using Floquet theory. A Fourier truncation of the monodromy operator is computed by solving the linearized ... More

Static structures of strained carbon chains:DFT-modeling vs classical modeling of the chain with Lennard-Jones potentialMar 13 2019We proved earlier that in the strained monoatomic chains with Lennard-Jones potential there can exist an equilibrium static bi-structure, which corresponds to N - 1 equal short interatomic bonds and one long bond with inversion in its center (N is the ... More

Nonlinear management of topological solitons in a spin-orbit-coupled systemMar 13 2019We consider possibilities to control dynamics of solitons of two types, maintained by the combination of cubic attraction and spin-orbit coupling (SOC) in a two-component system, namely, semi-dipoles (SDs) and mixed modes (MMs), by making the relative ... More

Statistical properties of nonlinear stage of modulation instability in fiber opticsMar 12 2019We present an optical fiber experiment in which we examine the space-time evolution of a modulationally unstable plane wave initially perturbed by a small noise. Using a recirculating fiber loop as experimental platform, we report the single-shot observation ... More

Symmetry breaking with opposite stability between bifurcated asymmetric solitons in parity-time-symmetric potentialsMar 12 2019We report a new type of symmetry-breaking bifurcation of solitons in optical systems with parity-time-symmetric potentials. In this bifurcation, the two bifurcated branches of asymmetric solitons exhibit opposite stability, which contrasts all previous ... More

Spin-orbit coupled polariton condensates in a radially-periodic potential: Multiring vortices and rotating solitonsMar 12 2019We address evolution of a spinor polariton condensate in radially periodic potentials. Such potentials allow for the observation of novel nonlinear excitations and support a variety of dynamically stable soliton states never demonstrated before in polariton ... More

Vortex soliton in a cold atomic gas via electromagnetically induced transparencyMar 08 2019We investigate the formation and propagation of vector vortex solitons (VS) and unipolar soliton (US) in a cold atomic gas with Bessel lattices (BLs). The system we consider is a cold, coherent atomic gas with a tripod or multipod level configuration. ... More

Duality Between Dirac Fermions in Curved Spacetime and Optical solitons in Non-Linear Schrodinger Model: Magic of $1+1$-Dimensional BosonizationMar 08 2019Bosonization in curved spacetime maps massive Thirring model (self-interacting Dirac fermions) to a generalized sine-Gordon model, both living in $1+1$-dimensional curved spacetime. Applying this duality we have shown that the Thirring model fermion, ... More

What kinds of KdV-type equations are allowed by an uneven bottomMar 07 2019In this study, we give a survey of derivations of KdV-type equations with an uneven bottom for several cases when small (perturbation) parameters $\alpha, \beta, \delta$ are of different orders. Two kinds of new second order wave equations: the \emph{extended ... More

Controlled Generation of Dark-Bright Soliton Complexes in Two-Component and Spinor Bose-Einstein CondensatesMar 07 2019We report on the controlled creation of multiple soliton complexes of the dark-bright type in one-dimensional two-component, three-component and spinor Bose-Einstein condensates. The formation of these states is based on the so-called matter wave interference ... More

Instability of $H^1$-stable peakons in the Camassa-Holm equationMar 06 2019It is well-known that peakons in the Camassa-Holm equation are $H^1$-orbitally stable thanks to the presence of conserved quantities and properties of peakons as constrained energy minimizers. By using the method of characteristics, we prove that piecewise ... More

Bifurcation of Gap Solitons in Coupled Mode Equations in $d$ DimensionsMar 06 2019We consider a system of first order coupled mode equations in $\mathbb{R}^d$ describing the envelopes of wavepackets in periodic media. Under the assumptions of a spectral gap and a generic assumption on the dispersion relation at the spectral edge, we ... More

On time relaxed schemes and formulations for dispersive wave equationsMar 06 2019The numerical simulation of nonlinear dispersive waves is a central research topic of many investigations in the nonlinear wave community. Simple and robust solvers are needed for numerical studies of water waves as well. The main difficulties arise in ... More

Evolution of wave pulses in fully nonlinear shallow-water theoryMar 05 2019We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the dispersive shock ... More

Self-similar and disordered front propagation in a radial Hele-Shaw channel with time-varying cell depthMar 03 2019The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plates can readily drive complex interfacial pattern formation known as viscous fingering. We focus on a modified system suggested recently by [1], in which the ... More

Fluxon interaction with the finite-size dipole impurityMar 02 2019Interaction of the fluxon with the finite size dipole impurity in the long Josephson junction is investigated. The impurity has polarity and will be referred to as a {\it dipole} impurity because it also has a direction and, consequently, changes its ... More

Short-distance propagation of nonlinear optical pulsesFeb 28 2019We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a defocusing nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be ... More

Generalized ballistic-conductive heat conduction in isotropic materialsFeb 28 2019The general isotropic constitutive equations of heat conduction with second sound and ballistic propagation in isotropic materials is given using Non-Equilibrium Thermodynamics with Internal Variables (NET-IV). The consequences of Onsager reciprocity ... More

Transparent nonlinear networksFeb 26 2019We consider the reflectionless transport of solitons in networks. The system is modeled in terms of the nonlinear Schr\"odinger equation on metric graphs, for which transparent boundary conditions at the branching points are imposed. This allows to derive ... More

A purely Kerr nonlinear model admitting flat-top solitonsFeb 25 2019We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including fundamental ones, ... More

Rogue Quantum Harmonic OscillationsFeb 23 2019We show the existence and investigate the dynamics and statistics of rogue oscillations (standing waves) generated in the frame of the nonlinear quantum harmonic oscillator (NQHO). With this motivation, in this paper, we develop a split-step Fourier scheme ... More

New Frontiers in Multidimensional Self-Trapping of Nonlinear Fields and MatterFeb 23 2019We review the state of the art and recently obtained theoretical and experimental results for two- and three-dimensional (2D and 3D) solitons and related states, such as quantum droplets, in optical systems, atomic Bose-Einstein condensates (BECs), and ... More

Stochastic ejection of nanocontact droplet solitons via drift instabilityFeb 21 2019The magnetic droplet soliton is a large amplitude, coherently precessing wave state that exists in ferromagnetic thin films with perpendicular magnetic anisotropy. To effectively sustain a droplet, magnetic damping can be locally compensated in a nanocontact ... More

Head-on collision of nonlinear solitary solutions to Vlasov-Poisson equationsFeb 20 2019Nonlinear solitary solutions to the Vlasov-Poisson set of equations are studied in order to investigate their stability by employing a fully-kinetic simulation approach. The study is carried out in the ion-acoustic regime for a collisionless, electrostatic ... More

Spontaneous generation of dark-bright and dark-antidark solitons upon quenching a particle-imbalanced bosonic mixtureFeb 19 2019We unveil the dynamical formation of multiple localized structures in the form of dark-bright and dark-antidark solitary waves that emerge upon quenching a one-dimensional particle-imbalanced Bose-Bose mixture. Interspecies interaction quenches drive ... More

Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical materialFeb 19 2019We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be described within ... More

Robust PT symmetry of two-dimensional fundamental and vortex solitons supported by spatially modulated nonlinearityFeb 19 2019The real spectrum of bound states produced by PT-symmetric Hamiltonians usually suffers breakup at a critical value of the strength of gain-loss terms, i.e., imaginary part of the complex potential. On the other hand, it is known that the PT-symmetry ... More

Gravitational perturbations from oscillons and transients after inflationFeb 18 2019We study the scalar and tensor perturbations generated by the fragmentation of the inflaton condensate into oscillons or transients after inflation, using nonlinear classical lattice simulations. Without including the backreaction of metric perturbations, ... More

A comparative study of bi-directional Whitham systemsFeb 18 2019In 1967, Whitham proposed a simplified surface water-wave model which combined the full linear dispersion relation of the full Euler equations with a weakly linear approximation. The equation he postulated which is now called the Whitham equation has ... More

Constant spacing in filament bundlesFeb 17 2019Assemblies of filaments appear in a wide range of systems: from biopolymer bundles, columnar liquid crystals, and superconductor vortex arrays; to familiar macroscopic materials, like ropes, cables and textiles. Interactions between the constituent filaments ... More

From self-organization in relativistic electron bunches to coherent synchrotron light: observation using a photonic time-stretch digitizerFeb 16 2019In recent and future synchrotron radiation facilities, relativistic electron bunches with increasingly high charge density are needed for producing brilliant light at various wavelengths, from X-rays to terahertz. In such conditions, interaction of electrons ... More

Solitons in inhomogeneous gauge potentials: integrable and nonintegrable dynamicsFeb 16 2019We introduce an exactly integrable nonlinear model describing the dynamics of spinor solitons in space-dependent matrix gauge potentials of rather general types. The model is shown to be gauge equivalent to the integrable system of vector nonlinear Schr\"odinger ... More

Effects of time-periodic forcing in a Cahn-Hilliard model for Langmuir-Blodgett transferFeb 15 2019The influence of a temporal forcing on the pattern formation in Langmuir-Blodgett transfer is studied employing a generalized Cahn-Hilliard model. The occurring frequency locking effects allow for controlling the pattern formation process. In the case ... More

Rogue Waves as Self-Similar Solutions on a Background: A Direct CalculationFeb 14 2019In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schr\"odinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson, and Zakharov ... More

Understanding the dynamics of biological and neural oscillator networks through mean-field reductions: a reviewFeb 14 2019Many biological and neural system can be seen as networks of interacting periodic processes. Importantly, the function of these networks depends on the collective dynamics: Synchrony of oscillations is probably amongst the most prominent examples of collective ... More

Understanding the dynamics of biological and neural oscillator networks through mean-field reductions: a reviewFeb 14 2019Feb 27 2019Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, the function of these networks depends on the collective dynamics: Synchrony of oscillations is probably amongst the most prominent examples of ... More

Impact of high-order effects on soliton explosions in the complex cubic-quintic Ginzburg-Landau equationFeb 13 2019We investigate the impact of higher-order nonlinear and dispersive effects on the onset of soliton explosions in the complex cubic-quintic Ginzburg-Landau equation. We show how the interplay of the high order effects (HOEs) results in the splitting of ... More

Factorization of KdV Schrödinger operators using differential subresultantsFeb 13 2019We address the classical factorization problem of a one dimensional Schr\"odinger operator $-\partial^2+u-\lambda$, for a stationary potential $u$ of the KdV hierarchy but, in this occasion, a "parameter" $\lambda$. Inspired by the more effective approach ... More

Ordered Hexagonal Patterns via Notch-Delta SignalingFeb 13 2019Many developmental processes in biology utilize Notch-Delta signaling to construct an ordered pattern of cellular differentiation. This signaling modality is based on nearest-neighbor contact, as opposed to the more familiar mechanism driven by the release ... More

Defect removal by solvent vapor annealing in thin films of lamellar diblock copolymersFeb 13 2019Solvent vapor annealing (SVA) is known to be a simple, low-cost and highly efficient technique to produce defect-free diblock copolymer (BCP) thin films. Not only can the solvent dilute the BCP segmental interactions, but also it can vary the characteristic ... More

Electro-Oxidation of p-Silicon in Fluoride-Containing Electrolyte: A Physical Model for the Regime of Negative Differential ResistanceFeb 12 2019When Si is anodically oxidized in a fluoride containing electrolyte, an oxide layer is grown. Simultaneously, the layer is etched by the fluoride containing electrolyte. The resulting stationary state exhibits a negative slope of the current-voltage characteristics ... More

Drift of spectrally stable shifted states on star graphsFeb 10 2019When the coefficients of the cubic terms match the coefficients in the boundary conditions at a vertex of a star graph and satisfy a certain constraint, the nonlinear Schr\"{o}dinger (NLS) equation on the star graph can be transformed to the NLS equation ... More

Salt Polygons are Caused by ConvectionFeb 10 2019From fairy circles to patterned ground and columnar joints, natural patterns spontaneously appear in many complex geophysical settings. Here, we consider the origins of polygons in the crusts of salt playa and salt pans. These beautifully regular features, ... More

Statistical Equilibrium of the Korteweg-de Vries and Benjamin-Ono Unidirectional Soliton ModelsFeb 09 2019The Korteweg-de Vries and Benjamin-Ono nonlinear wave equations can describe solitary waves, all of which propagate in the same direction and which emerge from collisions with their shapes unchanged. There are technical challenges to giving a description ... More

Topological Control of Synchronization Patterns: Trading Symmetry for StabilityFeb 08 2019Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is believed to enhance ... More

Cesium bright matter-wave solitons and soliton trainsFeb 08 2019A setup for studying bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is studied. Formation of soliton ... More

Cesium bright matter-wave solitons and soliton trainsFeb 08 2019Mar 05 2019A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton trains ... More

Nonlinear interactions between solitons and dispersive shocks in focusing mediaFeb 07 2019Nonlinear interactions in focusing media between traveling solitons and the dispersive shocks produced by an initial discontinuity are studied using the one-dimensional nonlinear Schrodinger equation. It is shown that, when solitons travel from a region ... More

Nonlinear interactions between solitons and dispersive shocks in focusing mediaFeb 07 2019Feb 16 2019Nonlinear interactions in focusing media between traveling solitons and the dispersive shocks produced by an initial discontinuity are studied using the one-dimensional nonlinear Schrodinger equation. It is shown that, when solitons travel from a region ... More

Chimera states in networks of locally and non-locally coupled SQUIDsFeb 06 2019Planar and linear arrays of SQUIDs (superconducting quantum interference devices), operate as nonlinear magnetic metamaterials in microwaves. Such {\em SQUID metamaterials} are paradigmatic systems that serve as a test-bed for simulating several nonlinear ... More

Controlled Generation of Chimera States in SQUID Metasurfaces using DC Flux GradientsFeb 05 2019SQUID (Superconducting QUantum Interference Device) metamaterials, subject to a time-independent (dc) flux gradient and driven by a sinusoidal (ac) flux field, support chimera states that can be generated with zero initial conditions. The dc flux gradient ... More

Supercontinuum Generation in Heavy-Metal Oxide Glass Based Suspended-Core Photonic Crystal FibersFeb 05 2019We investigate supercontinuum generation in several suspended-core soft-glass photonic crystal fibers pumped by an optical parametric oscillator tunable around 1550 nm. The fibers were drawn from lead-bismuth-gallium-cadmium-oxide glass (PBG-81) with ... More

Wavenumber Selection in Pattern Forming SystemsFeb 04 2019Wavenumber selection in pattern forming systems remains a long standing puzzle in physics. Previous studies have shown that external noise is a possible mechanism for wavenumber selection. We conduct an extensive numerical study of the noisy stabilized ... More

Lateral inhibition provides a unifying framework for spatiotemporal pattern formation in media comprising relaxation oscillatorsFeb 04 2019The collective dynamics seen in a wide variety of chemical, biological and ecological systems involve interactions between relaxation oscillators that typically involve fast activation process coupled with a slower inactivation. In this paper, we show ... More

Interactions of solitons with positive and negative masses: Shuttle motion and co-accelerationJan 31 2019We consider a possibility to realize self-accelerating motion of interacting states with effective positive and negative masses in the form of pairs of solitons in two-component BEC loaded in an optical-lattice (OL) potential. A crucial role is played ... More

Extreme events in forced oscillatory media in 0, 1 and 2 dimensionsJan 30 2019One of the open questions in the field of optical rogue waves is the relevance of the number of spatial dimensions in which waves propagate. Here we review recent results on extreme events obtained in 0, 1 and 2 spatial dimensions in the specific context ... More

Dynamics of breathers in the Gardner hierarchy: universality of the variational characterizationJan 29 2019We present a new variational characterization of breather solutions of any equation of the \emph{focusing} Gardner hierarchy. This hierarchy is characterized by a nonnegative index $n$, and $2n+1$ represents the order of the corresponding PDE member. ... More

Networks with point like nonlinearitiesJan 29 2019We study static nonlinear waves in networks described by a nonlinear Schrodinger equation with point-like nonlinearities on metric graphs. Explicit solutions fulfilling vertex boundary conditions are obtained. Spontaneous symmetry breaking caused by bifurcations ... More

Calculated threshold of supratransmission phenomena in waveguide arrays with saturable nonlinearityJan 28 2019In this work, we consider a semi-infinite discrete nonlinear Schr\"odinger equation with saturable nonlinearity driven at one edge by a driving force. The equation models the dynamics of coupled photorefractive waveguide arrays. It has been reported that ... More

A Primordial Particle System in three dimensionsJan 27 2019This article describes the conversion of the two-dimensional Primordial Particle System into a threedimensional model that exhibits comparable features. We present the transformed model here in the form of a pseudocode implementation and detail the modifications ... More

Structured light in self-organized laser output patterns and nonlocal mapsJan 26 2019Feb 05 2019Spatial chaos as a phenomenon of ultimate complexity requires the efficient numerical algorithms. For this purpose iterative low-dimensional maps have demonstrated high efficiency. Natural generalization of Feigenbaum and Ikeda maps may include convolution ... More

Exact parity and time reversal symmetry invariant and symmetry breaking solutions for a nonlocal KP systemJan 25 2019A nonlocal Alice-Bob Kadomtsev-Petviashivili (ABKP) system with shifted-parities ($\hat{P}_s^x$ and $\hat{P}_s^y$ parities with shifts for the space variables $x$ and $y$) and delayed time reversal ($\hat{T}_d$, time reversal with a delay) symmetries ... More

Multi-kink scattering in the double sine-Gordon modelJan 23 2019We study collisions of two, three, and four kinks of the double sine-Gordon model. The initial conditions are taken in a special form in order to provide collision of all kinks in one point. We obtain dependences of the maximal energy densities on the ... More

Symmetry breaking of quantum droplets in a dual-core trapJan 20 2019We consider the dynamical model of a binary bosonic gas trapped in a symmetric dual-core cigar-shaped potential. The setting is modeled by a system of linearly-coupled one-dimensional Gross-Pitaevskii equations with the cubic self-repulsive terms and ... More

Evading Derrick's theorem in curved space: Static metastable spherical domain wallJan 20 2019A recent analysis by one of the authors\cite{Perivolaropoulos:2018cgr} has pointed out that Derrick's theorem can be evaded in curved space. Here we extend that analysis by demonstrating the existence of a static metastable solution in a wide class of ... More

A response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling wavesJan 16 2019Jan 24 2019In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic up in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical ... More

Enhanced nonreciprocal transmission through a saturable cubic-quintic nonlinear dimer defectJan 16 2019The transmission properties through a saturable cubic-quintic nonlinear defect attached to lateral linear chains is investigated. Particular attention is directed to the possible non-reciprocal diode-like transmission when the parity-symmetry of the defect ... More

Gauged $CP(2)$ first-order solitons with internal structuresJan 16 2019We study a gauged $CP(2)$ model containing an additional real scalar field which interacts with the electromagnetic one through a dielectric function multiplying the standard Maxwell's term. In such a context, we look for first-order rotationally symmetric ... More

First-order solitons with internal structures in an extended Maxwell-$CP(2)$ modelJan 16 2019Mar 01 2019We study a Maxwell-$CP(2)$ model coupled to a real scalar field through a dielectric function multiplying the Maxwell term. In such a context, we look for first-order rotationally symmetric solitons by means of the Bogomol'nyi algorithm, i.e. by minimizing ... More

Finite Gap Conditions and Small Dispersion Asymptotics for the Classical Periodic Benjamin-Ono EquationJan 13 2019For any smooth spatially-periodic solution of the Benjamin-Ono equation, the work of Nazarov-Sklyanin determines a dispersive action profile, a piecewise-linear function of an auxiliary real variable whose values are all conserved by the flow. In this ... More

Nonlinear Waves in an Experimentally Motivated Ring-shaped Bose-Einstein Condensate SetupJan 13 2019We systematically construct stationary soliton states in a one-component, two-dimensional, repulsive, Gross-Pitaevskii equation with a ring-shaped target-like trap similar to the potential used to confine a Bose-Einstein condensate in a recent experiment ... More

Cooperative event-based rigid formation controlJan 11 2019This paper discusses cooperative stabilization control of rigid formations via an event-based approach. We first design a centralized event-based formation control system, in which a central event controller determines the next triggering time and broadcasts ... More

Temporal dissipative solitons in time-delay feedback systemsJan 11 2019Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, auto-solitons, spot or pulse solutions, these states play an important role in data transmission using optical ... More

Early stage of integrable turbulence in 1D NLS equation: the semi-classical approach to statisticsJan 08 2019We examine statistical properties of integrable turbulence in the defocusing and focusing regimes of one-dimensional small-dispersion nonlinear Schrodinger equation (1D-NLSE). Specifically, we study the 1D-NLSE evolution of partially coherent waves having ... More

Edge and bulk dissipative solitons in modulated PT-symmetric waveguide arraysJan 08 2019We address dissipative soliton formation in modulated PT-symmetric continuous waveguide arrays composed from waveguides with amplifying and absorbing sections, whose density gradually increases (due to decreasing waveguide separation) either towards the ... More

Tail-free self-accelerating solitons and vorticesJan 08 2019Self-accelerating waves in conservative systems, which usually feature slowly decaying tails, such as Airy waves, have drawn great interest in studies of quantum and classical wave dynamics. They typically appear in linear media, while nonlinearities ... More

Stabilization of localized structures by inhomogeneous injection in frequency comb generatorsJan 08 2019We consider the formation of temporal localized structures or Kerr comb generation in a microresonator with inhomogeneities. We show that the introduction of even a small inhomogeneity in the injected beam widens the stability region of localized solutions. ... More

Vortex Pairs in the Discrete Nonlinear Schr{ö}dinger EquationJan 03 2019The aim of the present work is to examine the role of discreteness in the interaction of both co-winding and counter-winding vortices in the context of the nonlinear Schr{\"o}dinger equation. Contrary to the well-known rotation of same charge vortices, ... More

Discrete breathers in $φ^4$ and related modelsJan 02 2019We touch upon the wide topic of discrete breather formation with a special emphasis on the the $\phi^4$ model. We start by introducing the model and discussing some of the application areas/motivational aspects of exploring time periodic, spatially localized ... More

Random Switching near BifurcationsJan 01 2019The interplay between bifurcations and random switching processes of vector fields is studied. More precisely, we provide a classification of piecewise deterministic Markov processes arising from stochastic switching dynamics near fold, Hopf, transcritical ... More

Spacetime Symmetries, Invariant Sets, and Additive Subdynamics of Cellular AutomataDec 30 2018Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured, complex behaviors. ... More

On multiplicities of irreducibles in large tensor product of representations of simple Lie algebrasDec 28 2018The main result of this paper is the asymptotical formula for multiplicities of irreducible representations in large tensor products of finite dimensional representation of simple Lie algebras. As a consequence we derive the asymptotical distribution ... More

On multiplicities of irreducibles in large tensor product of representations of simple Lie algebrasDec 28 2018Mar 08 2019In this paper we study the asymptotic of multiplicities of irreducible representations in large tensor products of finite dimensional representations of simple Lie algebras and their statistics with respect to Plancherel and character probability measures. ... More

Optical solitons in near $\mathcal{PT}-$symmetric Rosen-Morse potentialDec 26 2018We investigate the existence of stable soliton solution in a system described by complex Ginzburg-Landau (CGL) equation with near parity reflection - time reversal ($\mathcal{PT}$) symmetric Rosen-Morse potential. In this study, the stability of solution ... More

Phase-space geometry of reaction--diffusion dynamicsDec 20 2018Experimental studies of protein pattern formation (both in vivo and in vitro) have stimulated new interest in the dynamics of reaction--diffusion systems. However, a comprehensive theoretical understanding of the dynamics of such highly nonlinear, spatially ... More

Bi-directional universal dynamics in a spinor Bose gas close to a non-thermal fixed pointDec 20 2018We numerically study the universal scaling dynamics of an isolated one-dimensional ferromagnetic spin-1 Bose gas. Preparing the system in a far-from-equilibrium initial state, simultaneous coarsening and refining is found to enable and characterize the ... More

Basic mechanisms of escape of a harmonically forced classical particle from a potential wellDec 20 2018In various models and systems involving the escape of periodically forced particle from the potential well, a common pattern is observed. Namely, the minimal forcing amplitude required for the escape exhibits sharp minimum for the excitation frequency ... More

Controlling Dispersive Hydrodynamic Wavebreaking in a Viscous Fluid ConduitDec 19 2018The driven, cylindrical, free interface between two miscible, Stokes fluids with high viscosity contrast have been shown to exhibit dispersive hydrodynamics. A hallmark feature of dispersive hydrodynamic media is the dispersive resolution of wavebreaking ... More

Stability of bubble-like fluxons in disk-shaped Josephson junctions in the presence of a coaxial dipole currentDec 19 2018We investigate analytically and numerically the stability of bubble-like fluxons in disk-shaped heterogeneous Josephson junctions. Using ring solitons as a model of bubble fluxons in the two-dimensional sine-Gordon equation, we show that the insertion ... More

Embedded solitons in the double sine-Gordon lattice with the next neighbor interactionsDec 19 2018Topological solitons can propagate without radiation in discrete media. These solutions are known as embedded solitons (ES). They come as isolated solutions and exist despite their resonance with the linear spectrum of the respective lattices. In this ... More

Swift-Hohenberg equation with third order dispersion for optical fiber cavityDec 17 2018We investigate the dynamics of a ring cavity made of photonic crystal fiber and driven by a coherent beam working near the resonant frequency of the cavity. By means of a multiple-scale reduction of the Lugiato-Lefever equation with high order dispersion, ... More

Nonlinear Dynamics of Spherical Shells Buckling under Step PressureDec 16 2018Feb 06 2019Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling phenomena. To capture ... More

Directional Soliton and Breather BeamsDec 14 2018Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the uni-directional nonlinear Schr\"odinger equation (NLSE). We report ... More

Solitary Waves of the Camassa-Holm Derivative Nonlinear Schrödinger equationDec 12 2018In this paper we examine a deformation of the derivative nonlinear Schr\"odinger (DNLS) equation, the so-called Camassa-Holm DNLS (CH-DNLS) equation. We use two asymptotic multiscale expansion methods to reduce this model to both the modified Korteweg-de ... More

Topological states in chiral active matter: dynamic blue phases and active half-skyrmionsDec 11 2018We numerically study the dynamics of two-dimensional blue phases in active chiral liquid crystals. We show that introducing contractile activity results in stabilised blue phases, while small extensile activity generates ordered but dynamic blue phases ... More

Collective dynamics of evanescently coupled excitable lasers with saturable absorberDec 10 2018We present a numerical study of the collective dynamics in a population of coupled excitable lasers with saturable absorber. At variance with previous studies where real-valued (lossy) coupling was considered, we focus here on the purely imaginary coupling ... More

Stochastic fluctuations and quasi-pattern formation in reaction-diffusion systems with anomalous transportDec 09 2018Jan 20 2019Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations, and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a generating-functional approach ... More

Enhanced mobility of high-frequency discrete breathers in a monatomic chain with odd anharmonicityDec 09 2018The mobility of high-frequency discrete breathers in monatomic chains with nonlinear interatomic potentials of the nearest neighbours is considered. It was found that the odd (cubic and fifth) anharmonicity strongly affects the mobility of breathers, ... More

Dynamics and stabilization of bright soliton stripes in the hyperbolic-dispersion nonlinear Schrödinger equationDec 05 2018We consider the dynamics and stability of bright soliton stripes in the two-dimensional nonlinear Schr\"odinger equation with hyperbolic dispersion, under the action of transverse perturbations. We start by discussing a recently proposed adiabatic-invariant ... More