Related papers: Soliton-like behaviour in non-integrable systems
Solitons - localized wave packets that travel without spreading - play a central role in understanding transport and properties of nonlinear systems, from optical fibers to fluid dynamics. In quantum many-body systems, however, such robust…
In the present work, we study, by means of a one-dimensional lattice model, the collective excitations corresponding to intra molecular ones of a chain like proteins. It is shown that such excitations are described by the Nonlinear…
We derive a system of nonpolynomial Schroedinger equations (NPSEs) for one-dimensional wave functions of two components in a binary self-attractive Bose-Einstein condensate loaded in a cigar-shaped trap. The system is obtained by means of…
We consider the nonlinear Schr\"odinger equation with a general nonlinearity. In dimension higher than 2, this equation admits travelling wave solutions with a fixed profile which is not the ground state. This kind of profiles are called…
In this paper, we primarily construct Darboux transformation(DT) of the nonlocal coupled modified complex integrable dispersionless (cm-CID) equation, which is first proposed by the connection with a nonlocal coupled modified complex short…
We present a first-principles derivation of the variational equations describing the dynamics of the interaction of a spatial soliton and a surface plasmon polariton (SPP) propagating along a metal/dielectric interface. The variational…
We address the degree of universality of the Fermi-Pasta-Ulam recurrence induced by multisoliton fission from a harmonic excitation by analysing the case of the semiclassical defocusing nonlinear Schrodinger equation, which models nonlinear…
One-parameter families of exact two-component solitary-wave solutions for interacting high-frequency (HF) and low-frequency (LF) waves are found in the framework of Zakharov-type models, which couple the nonlinear Schr\"odinger equation…
The soliton solution of the integrable coupled nonlinear Schrodinger equation (NLS) of Manakov type is investigated by using Zakharov-Shabat (ZS) scheme. We get the bright N-solitons solution by solving the integrable uncoupled NLS of…
We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the…
We take a soliton solution of a classical non-linear integrable equation and quench (suddenly change) its non-linearity parameter. For that we multiply the amplitude or the width of a soliton by a numerical factor $\eta$ and take the…
We demonstrate the existence of stable collective excitation in the form of "supersolitons" propagating through chains of solitons with alternating signs (i.e., Newton's cradles built of solitons) in nonlinear optical couplers, including…
A new class of soliton-like solutions is derived for the Grad-Shafranov (GS) equations. A mathematical analogy between the GS equation for MHD equilibria and the cubic Schr\"odinger (CS) equation for non-linear wave propagation forms the…
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…
We investigate theoretically soliton excitations and dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in two and three dimensional optical lattices. We derive equations of nonlinear hydrodynamics in the…
This article is the first one in a suite of three articles exploring connections between dynamical systems of St\"{a}ckel-type and of Painlev\'{e}- type. In this article we present a deformation of autonomous St\"{a}ckel-type systems to…
A nonlocal nonlinear Schr\"odinger (NLS) equation was recently found by the authors and shown to be an integrable infinite dimensional Hamiltonian equation. Unlike the classical (local) case, here the nonlinearly induced "potential" is $PT$…
We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems…
The Korteweg-de Vries (KdV) equation governs the propagation of nonlinear internal and surface gravity waves in shallow ocean environments, where the balance between nonlinear steepening and frequency-dependent dispersion produces solitons.…
We look for solutions to derivative nonlinear Schrodinger equations built upon solitons. We prove the existence of multi-solitons i.e. solutions behaving at large time as the sum of finite solitons. We also show that one can attach a kink…