Folded solitary waves of the Boiti–Leon–Pempinelli system

The folded solitary waves are the multivalued localized excitations. Traditionally, to describe these complicated structures, one needs to find the “universal” formula through the multilinear variable separation approach. In this paper, the Boiti–Leon–Pempinelli system is first reduced to the unsteady convection–diffusion equation according to the homogeneous balance principle. And then, the Lie group theory is applied to this equation and the similarity reduction equations, and the similarity solutions are obtained. Thus, the abundant folded solitary waves of the Boiti–Leon–Pempinelli system are investigated. These results illustrate that the multivalued structures can be derived through another skill.