Global smooth solutions for the nonlinear Schrödinger equation with magnetic effect

Analytical Soliton Solutions Modeling of Nonlinear Schrödinger Equation with the Dual Power Law Nonlinearity  

Introduction In this study, we use a newly proposed method based on the software structure of the maple, called the Khaters method, and will be introducing exponential, hyperbolic, and trigonometric solutions for one of the Schrödinger equations, called the nonlinear Schrödinger equation with the dual power law nonlinearity. Given the widespread use of the Schrödinger equation in physics and e...

Direct search for exact solutions to the nonlinear Schrödinger equation

A five-dimensional symmetry algebra consisting of Lie point symmetries is firstly computed for the nonlinear Schrödinger equation, which, together with a reflection invariance, generates two five-parameter solution groups. Three ansätze of transformations are secondly analyzed and used to construct exact solutions to the nonlinear Schrödinger equation. Various examples of exact solutions with c...

Variational solutions for the discrete nonlinear Schrödinger equation

The interaction and propagation of optical pulses in a nonlinear waveguide array is described by the discrete nonlinear Schrödinger equation i∂zψn = −D(ψn+1 + ψn−1 − 2ψn) − γ|ψn|ψn, (1) whereD is a dispersion (or diffraction) coefficient, and γ is a measure of the nonlinearity. By means of the variational approximation, we study the discrete soliton solutions of this equation. We use a trial fu...

Exact Multisoliton Solutions of General Nonlinear Schrödinger Equation with Derivative

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation.