Related papers: Soliton-like Solutions for Nonlinear Schroedinger …
An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schr\"{o}dinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the…
Dynamics of solitons is considered in the framework of an extended nonlinear Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped…
By introducing and solving two correlative constrained variational problems as well as spectrum analysis, an approach to fix soliton frequency from the prescribed mass for nonlinear Schr\"odinger equations is found, and an open problem in…
The dynamics of soliton and quasisoliton solutions of cubic third order nonlinear Schr\"{o}dinger equation is studied. The regular solitons exist due to a balance between the nonlinear terms and (linear) third order dispersion; they are not…
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 consider the Cauchy problem for the nonlinear Schroedinger eqiation with initial data close to a sum of N decoupled solitons. Under some suitable assumptions on the spectral structure of the one soliton linearizations we prove that for…
We study the behavior of the soliton solutions of the equation i((\partial{\psi})/(\partialt))=-(1/(2m)){\Delta}{\psi}+(1/2)W_{{\epsilon}}'({\psi})+V(x){\psi} where W_{{\epsilon}}' is a suitable nonlinear term which is singular for…
Solitons are ubiquitous in nature and play a pivotal role in the structure and dynamics of solutions of nonlinear propagation equations. In many instances where solitons exist, analytical expressions of these special objects are not…
We consider the linear vector Schr\"odinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik hierarchy and use this fact to derive the N-soliton…
We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where…
The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by…
We construct soliton solution of a variable coefficients nonlinear Schr\"odinger equation in the presence of parity reflection - time reversal $(\mathcal{PT})-$ symmetric Rosen-Morse potential using similarity transformation technique. We…
Nonlinearity in the Schr\"odinger equation gives rise to rich phenomena such as soliton formation, modulational instability, and self-organization in diverse physical systems. Motivated by recent advances in engineering nonlinear gauge…
In this paper we present soliton solutions of two coupled nonlinear Schodinger equations modulated in the bspace and time. The approach allows us to obatin solitons with large variety of solutions depending on the nonlinearity and the…
We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a…
The parametrically driven damped nonlinear Schr\"odinger equation serves as an amplitude equation for a variety of resonantly forced oscillatory systems on the plane. In this note, we consider its nodal soliton solutions. We show that…
This work deals with soliton solutions of the nonlinear Schroedinger equation with a diversity of nonlinearities. We solve the equation in a potential which oscillates in time between attractive and expulsive behavior, in the presence of…
We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a…
The time-dependent one-dimensional nonlinear Schr\"odinger equation (NLSE) is solved numerically by a hybrid pseudospectral-variational quantum algorithm that connects a pseudospectral step for the Hamiltonian term with a variational step…
Recently a variety of nonlocal integrable systems has been introduced that besides fields located at particlar space-time points simultaneously also contain fields that are located at different, but symmetrically related, points. Here we…