Bifurcations and Exact Traveling Wave Solutions of the Modified Nesterenko-Type Equation: A Dynamical System Approach

Abstract

For the modified Nesterenko-type equation, its traveling wave system is a singular nonlinear ordinary differential equation. We use the method of dynamical systems to investigate the bifurcations of phase portraits and the dynamical behavior of the solutions of the corresponding traveling system. By considering some integer number pairs [Formula: see text], we derive the exact explicit parametric representations for some bounded traveling wave solutions in the given parameter regions. We found more than 42 explicit exact parametric representations of the periodic solutions, periodic peakon solutions as well as compacton solutions.