New types of exact solutions for the fourth-order dispersive cubic-quintic nonlinear Schrodinger equation

In this study, we use two direct algebraic methods to solve a fourth-order dispersive cubic-quintic nonlinear Schrodinger equation, which is used to describe the propagation of optical pulse in a medium exhibiting a parabolic nonlinearity law. By using complex envelope ansatz method, we first obtain a new dark soliton and bright soliton, which may approach nonzero when the time variable approaches infinity. Then a series of analytical exact solutions are constructed by means of F-expansion method. These solutions include solitary wave solutions of the bell shape, solitary wave solutions of the kink shape, and periodic wave solutions of Jacobian elliptic function. (C) 2010 Elsevier Inc. All rights reserved.