斑图形成与孤子

We find that the recently introduced model of self-trapping supported by a spatially growing strength of a repulsive nonlinearity gives rise to robust vortex-soliton tori, i.e., three-dimensional vortex solitons, with topological charges S.…

The linear stability of steady-state periodic patterns of localized spots in $\R^2$ for the two-component Gierer-Meinhardt (GM) and Schnakenburg reaction-diffusion models is analyzed in the semi-strong interaction limit corresponding to an…

We study the propagation of stress waves through ordered 2D networks of granular chains. The quasi-particle continuum theory employed captures the acoustic pulse splitting, bending, and recombination through the network and is used to…

We discuss differences between the variational approach to solitons and the accessible soliton approximaion in a highly nonlocal nonlinear medium. We compare results of both approximations by considering the same system of equations in the…

There exists the threshold-sensitive dynamical transition between the uniform and the periodic growth modes in the domain growth of ascorbic acid crystals from its aqueous supersaturated solution film. The crystal growth induces the…

We study the escape of a chain of coupled units over the barrier of a metastable potential. It is demonstrated that a very weak external driving field with suitably chosen frequency suffices to accomplish speedy escape. The latter requires…

This article is concerned with pointwise growth and spreading speeds in systems of parabolic partial differential equations. Several criteria exist for quantifying pointwise growth rates. These include the location in the complex plane of…

We introduce one- and two-dimensional (1D and 2D) models of parity-time ($% \mathcal{PT}$) -symmetric couplers with the mutually balanced linear gain and loss applied to the two cores, and cubic-quintic (CQ) nonlinearity acting in each one.…

We demonstrate the existence of one and two-dimensional bright solitons in the Bose-Einstein condensate with repulsive dipole-dipole interactions induced by a combination of dc and ac polarizing fields, oriented perpendicular to the plane…

We study the effects of coupling between layers of stochastic neural field models with laminar structure. In particular, we focus on how the propagation of waves of neural activity in each layer is affected by the coupling. Synaptic…

The Comment by Quintero et al (arXiv:1309.1065[nlin.PS])does not dispute the central result of our paper [Phys. Rev. E {87}, 062114 (2013)] which is a theory explaining the interplay between thermal noise and symmetry breaking in the…

Strong retardation of ultrashort optical pulses, including their deceleration and stoppage in the form of Bragg solitons in a cascaded Bragg-grating (BG) structure, is proposed. The manipulations of the pulses are carried out, using…

For the one-dimensional nonlinear Schroedinger equation with a complex potential, it is shown that if this potential is not parity-time (PT) symmetric, then no continuous families of solitons can bifurcate out from linear guided modes, even…

The resonant scattering of gap solitons (GS) of the periodic nonlinear Schr\"odinger equation with a localized defect which is symmetric under the parity and the time-reversal (PT) symmetry, is investigated. It is shown that for suitable…

We show that dispersive shock waves resulting from the nonlinearity overbalancing a weak leading-order dispersion can emit resonant radiation owing to higher-order dispersive contributions. We analyze such phenomenon for the defocusing…

Swarms of large numbers of agents appear in many biological and engineering fields. Dynamic bi-stability of co-existing spatio-temporal patterns has been observed in many models of large population swarms. However, many reduced models for…

In many Hamiltonian systems, propagation of steadily travelling solitons or kinks is prohibited because of resonances with linear excitations. We show that Hamiltonian systems with resonances may admit an infinite number of travelling…

We present explicit forms of general breather (GB), Akhmediev breather (AB), Ma soliton (MS) and rogue wave (RW) solutions of the two component nonlinear Schr\"{o}dinger (NLS) equation, namely Manakov equation. We derive these solutions…

We report that infinite and semi-infinite lattices with spatially inhomogeneous self-defocusing (SDF)\ onsite nonlinearity, whose strength increases rapidly enough toward the lattice periphery, support stable unstaggered (UnST) discrete…

We introduce a simple model for implementing the concepts of quasi-energy and parametric resonances (PRs) in systems with the $\mathcal{PT}$ symmetry, i.e., a pair of coupled and mutually balanced gain and loss elements. The parametric (ac)…