A numerical solution and an exact explicit solution of the NLS equation - El-Sayed, SM; Kaya, D (Elsevier Science Inc, 2006)
We consider traveling wave solutions of the nonlinear Schrodinger (NLS for short) equation. In this paper by considering the decomposition scheme, we first obtain the exact solutions of the NLS equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique. The numerical solutions are compared with the known analytical solutions. Its remarkable accuracy is finally demonstrated in the study of some initial values of the NLS equation. (c) 2005 Elsevier Inc. All rights reserved.
Keywords: the decomposition method; nonlinear Schrodinger equation; traveling wave solutions; numerical results