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New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. (English) Zbl 0977.35094

Summary: New Jacobi elliptic functions are applied in the Jacobi elliptic function expansion method to construct the exact periodic solutions of nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this method and more shock wave solutions or solitary wave solutions can be got at their limit condition.

MSC:

35L70 Second-order nonlinear hyperbolic equations
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
35B10 Periodic solutions to PDEs
35C10 Series solutions to PDEs
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