Bifurcations and Exact Traveling Wave Solutions in Two Nonlinear Wave Systems

Abstract

This paper studies two nonlinear wave models. From the dynamical systems approach and using the singular traveling wave theory developed by [Li & Chen, 2007], all possible bounded solutions (solitary wave solutions, periodic wave solutions, as well as kink and anti-kink wave solutions) are obtained under different parameter conditions. More than 27 explicit exact parametric representations are derived. The new results complete the recent studies of [Rogers et al., 2020; Zayeda et al., 2020].