斑图形成与孤子

We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one. The model can be experimentally realized in several fields…

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the…

We consider a quantum analogue of black holes and white holes using Bose-Einstein condensates. The model is described by the nonlinear Schrodinger equation with a 'stream flow' potential, that induces a spatial translation to standing…

We examine the spectral properties of single and multiple matter-wave dark solitons in Bose-Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large-density limit…

We consider a propagation of transition fronts in one-dimensional chains with bi-stable nondegenerate on-site potential. If one adopts linear coupling in the chain and piecewise linear on-site force, then it is possible to develop…

We investigate the formation of optical localized nonlinear structures, evolving upon a non-zero background plane wave, in a dispersive quadratic medium. We show the existence of quadratic Akhmediev breathers and Peregrine solitary waves,…

We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on…

In the paper an interaction between a soliton and a traveling wave in the Coupled Nonlinear Schr\"odinger Equation (CNLSE) is considered. The force acting on the soliton can both push or pull the soliton depending on parameters of the…

We present new solitarywave solutions of the two-dimensional nonlinear Schrodinger equation on bounded domains (such as rectangles, circles, and annuli). These multipeak necklace solitary waves consist of several identical positive profiles…

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation,…

We examine the dynamics of strongly localized periodic solutions (discrete breathers) in two-dimensional array of coupled finite one-dimensional chains of oscillators. Localization patterns with both single and multiple localization sites…

The propagation of waves in the nonlinear acoustic metamaterials (NAMs) is fundamentally different from that in the conventional linear ones. In this article we consider two one-dimensional NAM systems featuring respectively a diatomic and…

We prove the existence of an infinite number of internal (shape) modes of sine-Gordon solitons in the presence of some inhomogeneous long-range forces, provided some conditions are satisfied.

We study a nonlocal diffusion equation approximating the dynamics of coupled phase oscillators on large graphs. Under appropriate assumptions, the model has a family of steady state solutions called twisted states. We prove a sufficient…

The dynamics of non-autonomous bright matter-wave solitons in Rabi coupled binary Bose-Einstein condensates is explored. By performing a unitary and similarity/lens-type transformation, we reduce the non-autonomous Gross-Pitaevskii equation…

In this paper the Turing pattern formation mechanism of a two component reaction-diffusion system modeling the Schnakenberg chemical reaction coupled to linear cross-diffusion terms is studied. The linear cross-diffusion terms favors the…

This paper is motivated by the recent demonstration of three-wave mixing based phononic frequency comb. While the previous experiments have shown the existence of three-wave mixing pathway in a system of two-coupled phonon modes, this work…

In the present work, we explore the existence, stability and dynamics of single and multiple vortex ring states that can arise in Bose-Einstein condensates. Earlier works have illustrated the bifurcation of such states, in the vicinity of…

Recently, a number of nonlocal integrable equations, such as the PT-symmetric nonlinear Schrodinger (NLS) equation and PT-symmetric Davey-Stewartson equations, were proposed and studied. Here we show that many of such nonlocal integrable…

We connect the theories of the deformation of elastic surfaces and phase surfaces arising in the description of almost periodic patterns. In particular, we show parallels between asymptotic expansions for the energy of elastic surfaces in…