New Doubly Periodic Solutions of Nonlinear EvolutionEquations via Weierstrass Elliptic Function Expansion Algorithm

A Weierstrass elliptic function expansion method and its algorithmare developed in this paper. The method changes the problem solvingnonlinear evolution equations into another one solving the correspondingsystem of nonlinear algebraic equations.With the aid of symbolic computation (e.g. Maple),the method is applied to the combined KdV-mKdV equation and(2+1)-dimensional coupled Davey-Stewartson equation.As a consequence, many new types ofdoubly periodic solutions are obtained in terms ofthe Weierstrass elliptic function. Jacobi ellipticfunction solutions and solitary wave solutions are also given as simplelimits of doubly periodic solutions.