2014•International Journal of Bifurcation and ChaosRequires access

Exact Cuspon and Compactons of the Novikov Equation

Jibin Li

Abstract

In this paper, we apply the method of dynamical systems to the traveling wave solutions of the Novikov equation. Through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system and exact cuspon wave solution, as well as a family of breaking wave solutions (compactons). We find that the corresponding traveling system of Novikov equation has no one-peakon solution.

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Key concepts: Novikov self-consistency principle, Phase portrait, Traveling wave, Peakon, Mathematics, Dynamical systems theory, Mathematical analysis, Dynamical system (definition)