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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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