The new periodic wave solutions for cubic nonlinear Schrdinger equation

The cubic nonlinear Schrdinger(CNLS)equation,which exist widely in some systems such as plasma physics,nonlinear optics etc,has been studied by using the Weierstrass elliptic function expansion method.With the aid of travelling wave transformation,the CNLS equation can be reduced to an ordinary differential equation.Then,the main step of this algorithm changes the problem solving an ordinary differential equation into another one solving the corresponding set of nonlinear algebraic equations.As a conclusion,some new doubly periodic wave solutions are obtained in terms of the Weierstrass elliptic function.Meanwhile,the corresponding Jacobi elliptic function solutions and the solitary wave solutions are derived in the limit case.The method has two virtues:one is the process can be performed in computerized symbolic computation system such as Mathematica.Another is the method can be also applied to many nonlinear differential equation(equations)in mathematical physics.