In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …

A split-step method is used to discretize the time variable for the numerical solution of the
nonlinear Schrödinger equation. The space variable is discretized by means of a finite …

We study the application of Runge-Kutta schemes to Hamiltonian systems of ordinary
differential equations. We investigate which schemes possess the canonical property of the …

We approximate the solutions of an initial-and boundary-value problem for nonlinear
Schrödinger equations (with emphasis on the 'cubic'nonlinearity) by two fully discrete finite …

We present a new numerical scheme for nonlinear Schrödinger type equations. The scheme
conserves the energy and charge of the systems and it is linearly implicit. Numerical …

We propose a compact split-step finite difference method to solve the nonlinear Schrödinger
equations with constant and variable coefficients. This method improves the accuracy of split …

In this paper, we consider the nonlinear Schrödinger equation u_t+iΔu-F(u)=0 in two
dimensions. We show, by an operator-theoretic proof, that the well-known Lie and Strang …

This book is mainly devoted to the dynamics of the one-dimensional nonlinear stochastic
waves. It contains a description of the basic mathematical tools as well as the latest results in …

In this paper, we present a new numerical scheme for the nonlinear Schrödinger equation.
This is a relaxation-type scheme that avoids solving for nonlinear systems and preserves …

In this work, we numerically investigate the influence of a homogeneous noise on the
evolution of solitons for the Korteweg–de Vries equation. Our numerical method is based on …