New exact Jacobi elliptic functions solutions for the generalized coupled Hirota-Satsuma KdV system. (English) Zbl 1200.35260

Summary: An generalized Jacobi elliptic functions expansion method with computerized symbolic computation is used for constructing more new exact Jacobi elliptic functions solutions of the generalized coupled Hirota-Satsuma KdV system. As a result, eight families of new doubly periodic solutions are obtained by using this method, some of these solutions are degenerated to solitary wave solutions and triangular functions solutions in the limit cases when the modulus of the Jacobi elliptic functions \(m \rightarrow 1\) or 0, which shows that the applied method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.


35Q53 KdV equations (Korteweg-de Vries equations)
35C10 Series solutions to PDEs
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35B10 Periodic solutions to PDEs
35C08 Soliton solutions
Full Text: DOI


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