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Existence and construction of compacton solutions. (English) Zbl 1068.35124
Summary: We show the existence of compacton structures created from genuinely nonlinear dispersive equations. We show that the compactons, the compactly supported solitary waves free of exponential wings that vanish outside a finite core, are formally constructed from the focusing branches of these equations. We further show that the defocusing branches of these models generate solitary patterns solutions with infinite slopes or cusps.

MSC:
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
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