Symmetry Reductions, Cte Method and Interaction Solutions for Sharma-Tasso-Olver-Burgers Equation

Abstract

In this paper, the Sharma-Tasso-Olver-Burgers (STOB) system is analyzed by the Lie point symmetry method. The hypergeometric wave solution of the STOB equation is derived by symmetry reductions. In the meantime, the consistent tanh expansion (CTE) method is applied to the STOB equation. An nonauto-Bäcklund (BT) theorem that includes the over-determined equations and the consistent condition is obtained by the CTE method. By using the nonauto-BT theorem, the interactions between one-soliton and the cnoidal wave, and between one-soliton and the multiple resonant soliton solutions, are constructed. The dynamics of these novel interaction solutions are shown both in analytical and graphical forms. The results are potentially useful for explaining ocean phenomena.