The homotopic mapping solutions for the generalized Schrödinger equation

This work is concerned on how to find the approximation solutions of the generalized Schrodinger equation by using the homotopic mapping method. First, we give the basic idea of Homotopic mapping method. In the following, we introduce a homotopic mapping, and make the generalized Schrodinger equation do a homotopic deformation, then we get the approximation solutions in given initial conditions. Finally we give two examples about derivative Schrodinger equation and Hirota equation to illustrate efficiency of this method, and the exact solutions of these equations can be solved in the condition of selecting proper auxiliary function v.