Dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation

In this work, we apply the bifurcation method of dynamical systems to investigate the underlying complex dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation. We identify all bifurcation conditions and phase portraits of the system in different regions of the three-dimensional parametric space, from which we present the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like (antikink-like) wave solutions, and compactons. Furthermore, we obtain their exact expressions and simulations, which can help us understand the underlying physical behaviors of traveling wave solutions to the equation.