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Solutions of compact and noncompact structures for nonlinear Klein-Gordon-type equation. (English) Zbl 1027.35119
Summary: The focusing and the defocusing branches of nonlinear Klein-Gordon-type equation \(KG(n,n)\) are considered. A framework is implemented to show that the first model exhibits compactons: solitons that do not have exponential tails, whereas the second model demonstrates solitary patterns solutions. The two variants of \(KG(n,n)\) equation are examined in one and higher dimensions. General formulas will be developed to present a fairly complete understanding of the solutions of compact and noncompact structures.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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