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The new extended Jacobian elliptic function expansion algorithm and its applications in nonlinear mathematical physics equations. (English) Zbl 1196.35193
Summary: More recently we have presented the extended Jacobian elliptic function expansion method and its algorithm to seek more types of doubly periodic solutions. Based on the idea of the method, by studying more relations among all twelve kinds of Jacobian elliptic functions. we further extend the method to be a more general method, which is still called the extended Jacobian elliptic function expansion method for convenience. The new method is more powerful to construct more new exact doubly periodic solutions of nonlinear equations. We choose the (2+1)-dimensional dispersive long-wave system to illustrate our algorithm. As a result, twenty-four families of new doubly periodic solutions are obtained. When the modulus m1 or 0, these doubly periodic solutions degenerate as soliton solutions and trigonometric function solutions. This algorithm can be also applied to other nonlinear equations.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
33E05Elliptic functions and integrals
35B10Periodic solutions of PDE
35Q51Soliton-like equations
68W30Symbolic computation and algebraic computation