Infinitely many solitary waves of an integrable equation with singularity

Little seems to be known about the solitary waves and their properties of the completely integrable equations with singularity. This paper addresses the solitary waves of an integrable equation based on the bifurcation method of dynamical systems. We highlight two interesting results on the solitary waves. First, for arbitrary wave speed, there do exist infinitely many solitary waves in the integrable equation, which are classified by their expressions and forms of motion. Second, we find a family of solitary waves whose profiles seem like tree stumps.