相关论文: On the soliton dynamics under a slowly varying med…
We have applied the transformation of the slow light equations to Liouville theory that we developed in our previous work, to study the influence of relaxation on the soliton dynamics. We solved the problem of the soliton dynamics in the…
Studied here is the large-time behavior of solutions of the Korteweg-de Vries equation posed on the right half-line under the effect of a localized damping. Assuming as in \cite{linares-pazoto} that the damping is active on a set…
The supercritical composition of a plasma model with cold positive ions in the presence of a two-temperature electron population is investigated, initially by a reductive perturbation approach, under the combined requirements that there be…
We show that advection-diffusion equations with porous media type diffusion and integrable initial data are globally solvable under very mild conditions. Some generalizations and related results are also given.
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
We investigate propagation of slow-light solitons in atomic media described by the nonlinear $\Lambda$-model. Under a physical assumption, appropriate to the slow light propagation, we reduce the $\Lambda$-scheme to a simplified nonlinear…
We generalize the Abstract Interpolation Lemma proved by the authors in [2]. Using this extension, we show in a more general context, the persistence property for the generalized Korteweg-de Vries equation, see (1.2), in the weighted…
The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Backlund transformation for the restricted flows (by V.B.…
We study large-amplitude, very oblique Alfv\'en waves at low $\beta$, with small gradient length scales, comparable to the ion inertial scale $d_i$. Such waves have large density fluctuations, and slight dispersion from finite-frequency and…
We study the nonlocal modified Korteweg-de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz-Musslimani type nonlocal reductions. We first find soliton solutions of the coupled mKdV system by using the Hirota direct method. Then…
The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual…
This work presents a stochastic analysis of fifth-order KdV soliton momentum distribution in a damping regime. An explicit representation of the soliton momentum associated with amplitude variation is derived in terms of a random time…
We show how the inverse scattering transform can be used as a convenient tool to derive the long-time asymptotics of shock waves for the Korteweg-de Vries (KdV) equation in the soliton region. In particular, we improve the results…
We study the non-equilibrium dynamics of solitons in model Hamiltonians for Peierls dimerized quasi-one dimensional conducting polymers and commensurate charge density wave systems. The real time equation of motion for the collective…
New two-component soliton solutions of the coupled high-frequency (HF) - low-frequency (LF) system, based on Schr\"odinger - Korteweg - de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the…
In this paper, we carry out a theoretical investigation on the propagation of spatio-temporal solitons (light bullets) in the nonlinear metamaterial waveguides. Our theoretical study is based on the formulation of Lagrangian variational…
The evolution of a solitary wave with very weak nonlinearity which was originally investigated by Miles [4] is revisited. The solution for a one-dimensional gravity wave in a water of uniform depth is considered. This leads to finding the…
Recently, optical soliton propagation in an intrinsic nonlinear graphene monolayer configuration has been discovered. However, optical soliton behavior in a free-standing graphene monolayer with defects has not yet been studied. The…
The excitation and evolution of Korteweg-de Vries (KdV) solitons in a dusty plasma medium are studied using Molecular Dynamics (MD) simulations. The dusty plasma medium is modelled as a collection of dust particles interacting through…
In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in…