Traveling wave solutions for Burgers-Sharma-Tasso-Olver equation with variable coefficients: the improved tanh-coth method vs. exp. function method

Abstract

In this paper, we investigate the Burgers-Sharma-Tasso-Olver equation (B-STO) with variable coefficients from the point of view of its traveling wave solutions using the improved tanh-coth method and the Exp. function method. We show that from the solutions of the B-STO equation obtained applying the first method we can derive solutions to the classical Burgers equation as well as solutions to classical Sharma-Tasso-Olver equation, both with variable coefficients. Mathematics Subject Classification: 35C05

Dynamics and Exact Traveling Wave Solutions of the Sharma–Tasso–Olver–Burgers Equation

“…Thus, the STOB equation is an integrable nonlinear evolution equation that is a combination of the well-known Burgers equation and the STO equation. From the point of view of either mathematics or physics (see Olver (1977) [2], Lian and Lou (2005) [3], He et al (2013) [4], Gomez and Hernandez (2017) [5], El-Rashidy (2020) [6] and Li (2019) [7]), the Burgers system and the Sharma-Tasso-Olver equation have been widely investigated using various effective methods, including the inverse scattering method, Lie group method, Hirota's bilinear method, etc. Lian and Lou (2005) [3] used the simple symmetry reduction procedure to obtain infinitely many symmetries and exact solutions with new soliton fission and fusion phenomena for the STO equation.…”

“…In particular, for the STOB equation, Yan and Lou (2020) [1] investigated soliton molecules and their fission and fusion phenomena by introducing a velocity resonance mechanism. Gomez and Hernandez (2017) [5] used the improved tanh-coth method, as well as the Exp-function method, to investigate the traveling wave solutions. However, to date, little is known about the geometric structure and dynamic behaviors of the traveling wave solutions of the STOB equation.…”