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New periodic solutions to a kind of nonlinear wave equations. (Chinese. English summary) Zbl 1202.35134

Summary: The Jacobi elliptic function expansion method is extended to the finite expansion for the applied Jacobi cosine elliptic function or the third kind of Jacobi elliptic function to construct new periodic solutions of nonlinear wave equations. The periodic solutions obtained by this method can be reduced to solitary wave solutions under a limit condition.

MSC:

35L70 Second-order nonlinear hyperbolic equations
33E05 Elliptic functions and integrals
35B10 Periodic solutions to PDEs
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