Bifurcations and highly nonlinear traveling waves in periodic dimer granular chains

Abstract

Communicated by T. SimosIn this study, the highly nonlinear waves in periodic dimer granular chains were investigated by the theory of dynamical system and the method of phase diagram analysis. The bifurcations of the different traveling waves in parameter space and those different traveling waves and its phase diagram were given. In addition, the existence of smooth and nonsmooth traveling wave solutions are shown and various sufficient conditions to guarantee the existence of the above solutions were listed.