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New solitary-wave special solutions with compact support for the nonlinear dispersive \(K(m,n)\) equations. (English) Zbl 1028.35131
Summary: The genuinely nonlinear dispersive \(K(m, n)\) equation, \(u_t+ (u^m)_x+ (u^n)_{xxx}= 0\), which exhibits compactons, solitons with compact support, is investigated. New solitary-wave solutions with compact support are developed. The specific cases, \(K(2, 2)\) and \(K(3, 3)\), are used to illustrate the pertinent features of the proposed scheme. An entirely new general formula for the solution of the \(K(m, n)\) equation is established, and the existing general formula is modified as well.

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