Abstract
Compactons were introduced as solutions of nonlinear dispersive partial differential equations. There exists a variety of third-order equations that support compacton solutions. We consider a generalized third-order nonlinear K(fm,gn) equation that generalizes Rosenau–Hyman K(m,n) equation, extended Rosenau–Pikovsky K(cosmu,cosnu) equation, logarithmic KdV equation, generalized Gardner, and several other third-order nonlinear dispersive equations. In this paper, we obtain conservation laws of the K(fm,gn) equation in the most generalized form of f(u) and g(u). Several exact solutions of various equations of the K(fm,gn) form are derived from these generalized conservation laws by using the double reduction theory.
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Schedule a callMore From: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena
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