Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1 + 1)-dimensional dispersive long wave equation

Abstract

Abstract Our Jacobi elliptic function rational expansion method is extended to be a more powerful method, called the extended Jacobi elliptic function rational expansion method, by using more general ansatz. The (1 + 1)-dimensional dispersive long wave equation is chosen to illustrate the approach. As a consequence, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. When the modulus m → 1, these doubly periodic solutions degenerate as soliton solutions. The method can be also applied to other nonlinear differential equations.