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Zbl 1082.65584
Wazwaz, Abdul-Majid
The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation. (English)
[J] Appl. Math. Comput. 167, No. 2, 1179-1195 (2005). ISSN 0096-3003

Summary: The nonlinear Klein-Gordon equation is used as a vehicle to employ the tanh method and the sine-cosine method to formally derive a number of travelling wave solutions. The study features a variety of solutions with distinct physical structures. The work shows that one method complements the other, and each method gives solutions of formal properties. The obtained solutions include compactons, solitons, solitary patterns, and periodic solutions.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35Q53 KdV-like equations
35Q51 Solitons
37K40 Soliton theory, asymptotic behavior of solutions

Keywords: Compactons; Solitons; Periodic solutions; Klein-Gordon equation; Sine-cosine method; tanh method; travelling wave solutions

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Zentralblatt MATH Berlin [Germany]