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The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation. (English) Zbl 1082.65584
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:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
37K40Soliton theory, asymptotic behavior of solutions
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