Related papers: General $N$-Dark Soliton Solutions of the Multi-Co…
We report results of the study of solitons in a system of two nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials(MMs). The same model applies to photonic…
The dark soliton solution of the Gross-Pitaevskii equation in one dimension has two parameters that do not change the energy of the solution: the global phase of the condensate wave function and the position of the soliton. These…
Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov…
There is a lack of knowledge about the topological invariants of non-linear $d$-dimensional systems with a periodic potential. We study these systems through a classification of the linearized NLS/GP equation around their soliton solutions.…
A model of soliton-defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for…
We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a "crystalline" configuration to that of a disordered state that can be characterized as a soliton "gas". As…
A quantum system in complex potentials obeying parity-time (PT ) symmetry could exhibit all real spectra, starting out in non-Hermitian quantum mechanics. The key physics behind a PT-symmetric system consists of the balanced gain and loss…
We consider a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces. As important particular case of these MNLS we obtain the Kulish-Sklyanin model. Some new reductions and their…
We analyze the Floquet-Bloch matter-wave spectrum of Bose-Einstein condensates loaded into single-periodic optical lattices and double-periodic superlattices. In the framework of the Gross-Pitaevskii equation, we describe the structure and…
We analyse the structure of the exact, dark and bright soliton solutions of the driven non-linear Schr\"odinger equation. It is found that, a wide class of solutions of the higher order non-linear Schr\"odinger equation with a source can…
The existence, stability, and dynamics of bound pairs of symbiotic matter waves in the form of dark-bright soliton pairs in two-component mixtures of atomic Bose-Einstein condensates is investigated. Motivated by the tunability of the…
Using a bidifferential graded algebra approach to integrable partial differential or difference equations, a unified treatment of continuous, semi-discrete (Ablowitz-Ladik) and fully discrete matrix NLS systems is presented. These equations…
Bilinear forms for some nonlinear partial difference equations(discrete soliton equations) are derived based on the results of singularity confinement. Using the bilinear forms, the N-soliton and algebraic solutions of the discrete…
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates (BECs). Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our…
In this letter we report the existence of nondegenerate fundamental bright soliton solution for coupled multi-component nonlinear Schr\"{o}dinger equations of Manakov type. To derive this class of nondegenerate vector soliton solutions, we…
Bright plane soliton solutions of an integrable (2+1) dimensional ($n+1$)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one…
We report results of systematic numerical studies of 2D matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution…
We consider the persistence and stability of dark solitons in the Gross-Pitaevskii (GP) equation with a small decaying potential. We show that families of black solitons with zero speed originate from extremal points of an appropriately…
The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N-coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry…
The general multi-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 and dark multi-soliton solution using inverse…