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We study soliton solutions for the Gross--Pitaevskii equation of the spinor Bose--Einstein condensates with hyperfine spin F=2 in one-dimension. Analyses are made in two ways: by assuming single-mode amplitudes and by generalizing Hirota's…
We analytically solved the higher-order nonlinear Schrodinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and investigated explicitly bright and dark solitary wave solutions. Periodic wave solutions are also…
We develop the analytical method of field momenta for analyzing the dynamics of optical vector solitons in photorefractive nonlinear media. First, we derive the effective evolution equations for the parameters of multi-component solitons…
Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the stat- ics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an…
The effects of long-range intermolecular interactions on characteristic features of soliton bound states, consisting of localized excitons and polaritons in molecular crystals interacting with a high-intensity optical field, are…
Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model which incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions…
We construct symmetry preserving and symmetry broken N-bright, dark and antidark soliton solutions of a nonlocal nonlinear Schr\"{o}dinger equation. To obtain these solutions, we use appropriate eigenfunctions in Darboux transformation (DT)…
A general form of $N$-dark soliton solutions of the multi-component Mel'nikov system is presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general…
We implement variational shortcuts to adiabaticity for optical pulse compression in an active nonlinear Kerr medium with distributed amplification and spatially varying dispersion and nonlinearity. Starting with the hyperbolic secant…
We present a stability analysis of a modified nonlinear Schroedinger equation describing the propagation of ultra-short pulses in negative refractive index media. Moreover, using methods of quantum statistics, we derive a kinetic equation…
In this paper, we propose an alternative approach to generate a new class of beating vector solitons. Unlike earlier procedures that use dark-bright or bright-dark soliton solutions to generate beating solitons, the method described here…
Using Painlev\'e analysis, the Hirota multi-linear method and a direct ansatz technique, we study analytic solutions of the (1+1)-dimensional complex cubic and quintic Swift-Hohenberg equations. We consider both standard and generalized…
Two different types of N=1 modified KdV equations are shown to possess $N$ soliton solutions. The soliton solutions of these equations are obtained by casting the equations in the bilinear forms using the supersymmetric extension of the…
We consider the ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schr\"{o}dinger equation with varying…
Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr\"oinger equation respectively. Multi-soliton solutions of the resulted…
In this paper, a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation is studied in liquid with gas bubbles. Based on the Hirota's bilinear form and symbolic computation, lump and interaction solutions between lump…
We discuss temporal dark solitons in confined nonuniform Bose condensates. As a kind of localized high excitation, these solitons can be viewed as macroscopic quasiparticles, having relative motion to the background condensate. We get an…
Driven optical cavities containing a nonlinear medium support stable dissipative solitons, cavity solitons, in the form of bright or dark spots of light on a uniformly-lit background. Broadening effects due to diffraction or group velocity…
In this paper, we introduce the reverse-space and reverse-space-time nonlocal discrete derivative nonlinear Schr\"odinger (DNLS) equations through the nonlocal symmetry reductions of the semi-discrete Gerdjikov-Ivanov equation. The…
The dynamics of light beams in the nonlinear optical media with periodically modulated in the longitudinal direction parity-time distribution of the complex refractive index is investigated. The possibility of dynamical stabilization of…