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General compactons solutions for the focusing branch of the nonlinear dispersive \(K(n,n)\) equations in higher-dimensional spaces. (English) Zbl 1027.35117

Summary: We study the focusing branch of the genuinely nonlinear dispersive \(K(n,n)\) equation that exhibits compactons: solitons with finite wavelengths. The equation is studied in one-, two- and three-dimensional spaces. General formulas for compactons solutions are developed for all positive integers \(n\), \(n<1\). We give formulas for compactons for even integers \(n\) and for compactons and anticompactons for odd integers \(n\), \(n>1\).

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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