Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE method. (English) Zbl 1089.35534

Wazwaz, A. M.

Comput. Math. Appl. 50, No. 10-12, 1685-1696 (2005).

Summary: New exact travelling wave solutions for the double sinh-Gordon equation and its generalized form are formally derived by using the tanh method and the variable separated ODE method. The Painlevé property \(v = e^{u}\) is employed to support the tanh method in deriving exact solutions. The work emphasizes the power of the methods in providing distinct solutions of different physical structures.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35K40	Second-order parabolic systems
35C05	Solutions to PDEs in closed form

Keywords:

traveling wave solutions; tanh method; variable separated ODE method; Painlevé property; double sinh-Gordon equation

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