Related papers: Soliton dynamics for the Schrodinger-Newton system
We investigate the modulational instability of nonlinear Schr{\"o}dinger equations with periodic variation of their coefficients. In particular, we focus on the case of the recently proposed, experimentally realizable protocol of Feshbach…
We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear…
We study the correspondence between modulational instability and types of fundamental nonlinear excitation in a nonlinear fiber with both third-order and fourth-order effects. Some stable soliton excitations are obtained in modulational…
Solitons play a fundamental role in dynamics of nonlinear excitations. Here we explore the motion of solitons in one-dimensional uniform Bose-Einstein condensates subjected to a spin-orbit coupling (SOC). We demonstrate that the spin…
The focusing nonlinear Schrodinger equation possesses special non-dispersive solitary type solutions, solitons. Under certain spectral assumptions we show existence and asymptotic stability of solutions with the asymptoic profile (as time…
We propose an experimentally relevant scheme to create stable solitons in a three-dimensional Bose-Einstein condensate confined by a one-dimensional optical lattice, using temporal modulation of the scattering length (through ac magnetic…
We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatio-temporal forcing in the form of a travelling wave modulation of a control parameter. We show that from strictly spatial resonance, it is…
The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is…
We define the concept of instability index of an isolated eigenvalue of a non-self-adjoint operator, and prove some of its general properties. We also describe a stable procedure for computing this index for Schroedinger operators in one…
Gaussians to study soliton behavior and blowup in the nonlinear Schrodinger equation in arbitrary dimension d and with arbitrary nonlinearity parameter kappa
Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and…
We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schr\"{o}dinger equation (NLSE), which includes the harmonic-oscillator (HO) potential and a random potential. The…
In this paper we investigate the dynamics of solitons occurring in the nonlinear Schroedinger equation when a parameter h->0. We prove that under suitable assumptions, the the soliton approximately follows the dynamics of a point particle,…
Following our previous work [J. Ieda, T. Miyakawa, M. Wadati, cond-mat/0404569] on a novel integrable model describing soliton dynamics of an F=1 spinor Bose--Einstein condensate, we discuss in detail the properties of the multi-component…
This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e., self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison…
Existence of a new class of soliton solutions is shown for higher order nonlinear Schrodinger equation, describing thrid order dispersion, Kerr effect and stimulated Raman scattering. These new solutions have been obtaiened by invoking a…
We propose a solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. The one-soliton solutions of the system, which have nested structures similar to fractals, are also proved. The…
The existence of ``dispersion-managed solitons'', i.e., stable pulsating solitary-wave solutions to the nonlinear Schr\"{o}dinger equation with periodically modulated and sign-variable dispersion is now well known in nonlinear optics. Our…
We provide some numerical computations for the soliton dynamics of the nonlinear Schr\"odinger equation with an external potential. After computing the ground state solution $r$ of a related elliptic equation we show that, in the…
We find the N-soliton solution at infinite theta, as well as the metric on the moduli space corresponding to spatial displacements of the solitons. We use a perturbative expansion to incorporate the leading 1/theta corrections, and find an…