A General Jacobi Elliptic Function Rational Expansion Method and Its Applications in Nonlinear Wave Equations

A new general Jacobi elliptic function rational expansion method, which is more general and powerful than the tanh method, the sine-cosine method, the Jacobi elliptic function method and the extended Jacobi elliptic function method, and the extended Jacobi elliptic function rational expansion method, is proposed to construct abundant rational formal exact doubly periodic wave solutions of systems of nonlinear wave equations. When the modulus m $\rightarrow$ $1$ or $0$, these rational formal doubly periodic solutions degenerate as solitary wave solutions and trigonometric function solutions. And the method can be automatically carried out in computer.