2009•International Journal of Bifurcation and ChaosRequires access

BREAKING WAVE SOLUTIONS TO THE SECOND CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS

Jibin Li, Xiaohua Zhao, Guanrong Chen

Abstract

The existence of breaking wave solutions of the second class of singular nonlinear wave equations is proved by methods from the dynamical systems theory. For the second class of singular nonlinear traveling wave equations, dynamical behaviors of the traveling wave solutions are completely classified and thoroughly discussed. Corresponding to some bounded orbits of the traveling systems, exact parametric representations of traveling wave solutions are derived within different parameter regions of the parameter space.

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Key concepts: Traveling wave, Nonlinear system, Mathematical analysis, Mathematics, Class (philosophy), Parametric statistics, Bounded function, Dynamical systems theory