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Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. (English) Zbl 0972.35062
Summary: A Jacobi elliptic function expansion method, which is more general than the hyperbolic tangent function expansion method, is proposed to construct the exact periodic solutions of nonlinear wave equations. It is shown that the periodic solutions obtained by this method include some shock wave solutions and solitary wave solutions.
MSC:
35L05Wave equation (hyperbolic PDE)
35L70Nonlinear second-order hyperbolic equations
35A08Fundamental solutions of PDE