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