Auxiliary equation method and new solutions of Klein-Gordon equations. (English) Zbl 1143.35341

Summary: Many new types of exact solutions of an auxiliary ordinary differential equation are introduced. They are used to generate new exact travelling wave solutions of the quadratic and the cubic nonlinear Klein-Gordon equations. This approach is also applicable to a large variety of nonlinear partial differential equations.


35L70 Second-order nonlinear hyperbolic equations
35C05 Solutions to PDEs in closed form
Full Text: DOI


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