斑图形成与孤子
A major challenge in the theoretical modeling of double-slit interferometry involving matter-wave fields is the appropriate waveform to be assigned to this field. While all the studies carried out to date on this issue deal with variational…
We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and current conservation. Traveling wave solutions for star and tree…
We study collisions of moving nonlinear-Schr\"{o}dinger solitons with a $\mathcal{PT}$-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and,…
We study symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regime of a single-mode fiber. Key characteristics of such multi-peak solitons, as the formation mechanism, propagation…
In the Gray-Scott reaction-diffusion system one reactant is constantly fed in the system, another reactant is reproduced by consuming the supplied reactant and also converted to an inert product. The rate of feeding one reactant in the…
Several mathematical and physical aspects of waves on finite background are reported in this article. The evolution of the complex wave packet envelope of these type of waves is governed by the focussing-type of the nonlinear…
We describe linear and nonlinear modes in a ring-shaped waveguide with localized gain and dissipation modeled by two Dirac $\delta$ functions located symmetrically. The strengths of the gain and dissipation are equal, i.e., the system obeys…
We study the existence and stability of fundamental bright discrete solitons in a parity-time (PT)-symmetric coupler composed by a chain of dimers, that is modelled by linearly coupled discrete nonlinear Schrodinger equations with gain and…
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic…
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for…
It is well known that Akhmediev breathers of the nonlinear cubic Schrodinger equation can be superposed nonlinearly via the Darboux transformation to yield breathers of higher order. Surprisingly, we find that the peak height of each…
The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model…
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis…
The maximal energy density that can be achieved in the collisions of the particle-like wave trains in the $\phi^4$ model has been investigated numerically for different wave train parameters. From these results the prediction is made on how…
We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson [36], is known to support stationary and travelling bumps of localised…
Families of soliton pairs, namely vector solitons, are found within the context of a coupled nonlocal nonlinear Schrodinger system of equations, as appropriate for modeling beam propagation in nematic liquid crystals. In the focusing case,…
We compare numerical solutions to the full field equations to simplified approaches based on implementing three collective coordinates for kink-antikink interactions within the $\varphi^4$ and $\phi^6$ models in one time and one space…
In this paper, we study the smooth transition from solitons to solitary waves in localization, relation between energy and velocity, propagation and scattering property in the Fermi-Pasta-Ulam lattice analytically and numerically. A soliton…
A multiple scale model of the nonlinearly coupled KdV equations is established to predict mechanism of interaction of equatorial Rossby waves and barotropic waves in certain case. Analytically, predicted precursor radiation is a…
This paper presents new findings concerning the dynamics of the slow height variations in surfaces produced by the two-dimensional isotropic Kuramoto-Sivashinsky equation with an additional nonlinear term. In addition to the disordered…