Doubly periodic solutions of the coupled scalar field equations

Some doubly periodic (Jacobi elliptic function) solutions of the coupled Schrödinger–Boussinesq (KdV) equations are presented in closed form. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solution to construct doubly periodic solutions of the coupled equations. When the module m→1, these solutions degenerate to the exact solitary wave solutions of the coupled equations.