Exact solutions for Calogero–Bogoyavlenskii–Schiff equation using symmetry method

Abstract

In this paper, the symmetry method has been carried over to the Calogero–Bogoyavlenskii–Schiff equation. The infinitesimal symmetries and six basic linear combinations of the vector fields are determined, this leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations are eventually reduced to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions.