Abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional integrable Davey–Stewartson-type equation via a new method

Abstract

Our extended Jacobi elliptic function expansion method is further improved to be a more powerful method, which is still called the extended Jacobi elliptic function expansion method, by using 12 Jacobi elliptic functions. The new (2+1)-dimensional integrable Davey–Stewartson-type is chosen to illustrate the approach. As a consequence, 24 families of Jacobi elliptic function solutions are obtained. When the modulus m→1, these doubly periodic solutions degenerate as soliton solutions. The method can be also applied to other nonlinear differential equations.