A simple transformation for nonlinear waves. (English) Zbl 1037.35504

Summary: A transformation method is proposed to establish a relation between linear and nonlinear wave theories. We show that this transformation can be obtained from the sine-Gordon equation. This new method is simpler than the hyperbolic tangent method in solving differential equations and can be used to get more solutions to a wide class of nonlinear wave equations.


35Q53 KdV equations (Korteweg-de Vries equations)
35L70 Second-order nonlinear hyperbolic equations
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