Related papers: Stability and dynamics of two-soliton molecules
An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models…
A vortex molecule is a topological excitation in two coherently coupled superfluids consisting of a vortex in each superfluid connected by a domain wall of the relative phase, also known as a Josephson vortex. We investigate the dynamics of…
We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically…
We derive the equations governing the motion of Kerr solitons in pair waveforms. Recent experiments in microresonators have studied a variety of interaction effects in multisoliton waveforms, including collisions and formation of soliton…
We consider motion of a "magnetic'' soliton in two-component condensates along a non-uniform and time-dependent backgrounds in framework of the Hamiltonian mechanics. Our approach is based on generalization of Stokes' remark that soliton's…
We study the Gross-Pitaevskii equation with a delta function potential, $ q \delta_0 $, where $|q|$ is small, and analyze the solutions for which the initial condition is a soliton with initial velocity $v_0$. We show that up to time $ (|q|…
Dynamics of the Davydov's soliton in an external oscillating in time magnetic field is studied analytically. It is shown that in a field perpendicular to the molecular chain axis, soliton wavefunction is a product of the electron plane wave…
We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the…
In Molecular Dynamics (MD), the forces applied to atoms derive from potentials which describe the energy of bonds, valence angles, torsion angles, and Lennard-Jones interactions of which molecules are made. These de finitions are classic;…
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation with small multiplicative forcing. Forcing breaks the conservative structure of the KdV equation, leading to substantial changes in energy over long…
We consider the nonlinear Klein Gordon Maxwell system on four dimensional Minkowski space-time. For appropriate nonlinearities the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons…
Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is…
We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent…
We study the statics and dynamics of a binary dipolar Bose-Einstein condensate soliton for repulsive inter- and intraspecies contact interactions with the two components subject to different spatial symmetries $-$ distinct…
The dynamics of the soliton in a self-attractive Bose-Einstein condensate under the gravity are investigated. First, we apply the inverse scattering method, which gives rise to equation of motion for the center-of-mass coordinate of the…
This paper is concerned with the interaction of two solitons of nearly equal speeds for the (BBM) equation. This work is an extension of the results obtained in arXiv:0910.3204 by the same authors, addressing the same question for the…
We study the stability and dynamics of vortices in two-species condensates using a two mode model. The recent experimental results obtained at JILA (M. R. Matthews, {\em et al.}, Phys. Rev. Lett. 83 (1999) 2498) and theoretical predictions…
Bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using…
We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schr\"{o}dinger and Korteweg-de Vries equations under random perturbations of…
We sketch two rigorous proofs of the stability of the hydrogen molecule in quantum mechanics. The first one is based on an extrapolation of variational estimates of the groundstate energy of a positronium molecule to arbitrary mass ratios.…