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General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations $$mK(n,n)$$ in higher dimensional spaces. (English) Zbl 0996.35065
Summary: We present a general and unified approach for analyzing the genuinely nonlinear dispersive $$mK(n,n)$$ equations. The focusing branch exhibits compactons: solitons with finite wave lengths, whereas the defocusing branch supports solutions with solitary patterns. The work formally shows how to construct compact and noncompact solutions for $$mK(n,n)$$ equations in one-, two- and three-dimensional spatial domains. Two distinct general formulae for each model, that are of substantial interest, are developed for all positive integers $$n$$, $$n>1$$.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
##### Keywords:
compacton; solitons; KdV equation; nonlinear dispersive equation
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