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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:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
Software:
MACSYMA
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References:
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