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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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