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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
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