斑图形成与孤子

We consider exact and asymptotic solutions of the stationary cubic nonlinear Schr\"odinger equation (NLSE) on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation…

The paper is devoted to nonlinear localized modes ("gap solitons") for the spatially one-dimensional Gross-Pitaevskii equation (1D GPE) with a periodic potential and repulsive interparticle interactions. It has been recently shown (G. L.…

In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…

We consider the influence of optical and temperature-dependent atomic fluctuations on the formation and propagation of optical vortex solitons in dense media realized as hollow-core optical fibers filled with a cold atomic gas in presence…

Interference patterns associated with soliton-soliton interaction are investigated in detail. We find that the temporal and spatial interference patterns exhibit quite different characteristics. The period of the spatial interference…

We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can prove power-law asymptotics for the speed, with exponent…

We investigate the dynamics of the localized nonlinear matter wave in spin-1 Bose-Einstein condensates with trapping potentials and nonlinearities dependent on time and space. We solve the three coupled Gross-Pitaevskii equation by…

Nonlocality is a key feature of many physical systems since it prevents a catastrophic collapse and a symmetry-breaking azimuthal instability of intense wave beams in a bulk self-focusing nonlinear media. This opens up an intriguing…

Evaluation of analytical solutions of non-linear partial differential equations (both classical and fractional) is a rising subject in Applied Mathematics because its applications in Physical biological and social sciences. In this paper we…

We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…

We study mechanisms for wavenumber selection in a minimal model for run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces the existence of a plethora of traveling- and standing-wave patterns, as well as a subtle…

We develop a method for achieving scalable transmission stabilization and switching of $N$ colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of…

We present the study of the dark soliton dynamics in an inhomogenous fiber by means of a variable coefficient modified nonlinear Schr\"{o}dinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and…

Early results concerning the shape and stability of ion acoustic waves are generalized to propagation at an angle to the magnetic field lines. Each wave has a critical angle for stability. Known soliton results are recovered as special…

Exact bright, dark, antikink solitary waves and Jacobi elliptic function solutions of the generalized Benjamin-Bona-Mahony equation with arbitrary power-law nonlinearity will be constructed in this work. The method used to carry out the…

A stable nonlinear wave packet, self-localized in all three dimensions, is an intriguing and much sought after object in nonlinear science in general and in nonlinear photonics in particular. We report on the experimental observation of…

Given any background (or seed) solution of the nonlinear Schr\"odinger equation, the Darboux transformation can be used to generate higher-order breathers with much greater peak intensities. The Darboux transformation is generic in…

Kuramoto and Battogtokh [Nonlinear Phenom. Complex Syst. 5, 380 (2002)] discovered chimera states represented by stable coexisting synchrony and asynchrony domains in a lattice of coupled oscillators. After reformulation in terms of local…

We experimentally demonstrate the feasibility of visualizing stress waves propagating in plates using air-coupled acoustic emission sensors. Specifically, we employ a device that embeds arrays of microphones around an optical lens in a…

Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…