Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schrodinger's equation with Kerr law nonlinearity

In this Letter, we investigate the perturbed nonlinear Schrodinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as Is increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.