Bifurcations and Exact Solutions in a Symmetric Triple-Well Model

In this paper, we consider the bifurcations and exact solutions in the symmetric [Formula: see text] triple-well model. By using the method of dynamical systems, we obtain bifurcations of the phase portraits of the corresponding planar dynamical system under different parameter conditions. Corresponding to some level curves, we derive possible exact explicit parametric representations of the smooth periodic solution, homoclinic solutions, as well as heteroclinic solutions.