Lie Algebra Classification, Conservation Laws and Invariant Solutions for a Generalization of the Sharma–Tasso–Olever Equation

Abstract

Sharma–Tasso–Olever equation is an interesting partial differential equation with multiple associated studies. This type of nonlinear evolution equation, has an important role in understanding the nonlinear physical phenomena, for instance this equation describe the fission and fusion phenomena for solitons and sometimes solitary waves. In the present paper we investigate a generalization of that equation. For this purpose the complete classification of the Lie group symmetries is calculated. Moreover, we get the associated optimal system, from that, we reduced the original equation to an ordinary differential equation and hence implicit solution are constructed. Furthermore, conservation laws using the Ibragimov’s method are derived. Finally, we classify the Lie algebra for the symmetry group and its optimal system.