Doubly periodic solutions for a class of nonlinear coupled equations and two related physical models

By introducing parameters hypothesis method and using the Jacobi elliptic function expansion method, four kinds of doubly periodic (Jacobi elliptic function) solutions for a class of nonlinear coupled equations are presented in closed form. Subsequently, some doubly periodic solutions for two related physical models are obtained conveniently. When the module m→1, these solutions exactly degenerate to the solitary wave solutions.