The (G′/G)-expansion method and travelling wave solutions for a higher-order nonlinear schrödinger equation

The higher-order nonlinear Schrödinger equation is reduced to a nonlinear ordinary differential equation (ODE) by using a simple transformation, various solutions of the nonlinear ODE are obtained by the (G′/G)-expansion method proposed recently. With the aid of solutions of the nonlinear ODE more explicit travelling wave solutions involving two arbitrary parameters of the higher-order nonlinear Schrödinger equation are found out. The travelling waves are expressed by the hyperbolic functions, trigonometric functions and rational functions. When the parameters are taken as special values the solitary waves are also derived from the travelling waves.