Symmetry reduction and explicit solutions of the (2+1)-dimensional Boiti–Leon–Pempinelli system

Through the standard truncated Painlevé expansion of the Boiti–Leon–Pempinelli equation, the residual symmetry is localized in the properly prolonged system with the Lie point symmetry vector. Some different transformation invariances are derived through the obtained symmetries. At the same time, the symmetry of the equation is also derived utilizing the Clarkson–Kruskal direct method. From which, through solving the characteristic equations, several types of the explicit reduction solutions that related the hyperbolic tangent function are obtained. Finally, some kink-type soliton excitations are depicted from one of them.