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The extended Jacobian elliptic function expansion method and its application in the generalized Hirota-Satsuma coupled KdV system. (English) Zbl 1037.35074
Summary: An extended Jacobian elliptic function expansion method is used to construct new exact doubly periodic solutions of the generalized Hirota-Satsuma coupled KdV system by using symbolic computation. As a result, sixteen families of new doubly periodic solutions are obtained. The method is also applied to other higher-dimensional nonlinear evolution equations in mathematical physics.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
37K20Relations of infinite-dimensional systems with algebraic geometry, etc.
35C05Solutions of PDE in closed form