| Summary: | Nonlinear Burgers equation with variable coefficients (BEVC) which involves mathematical physics in plasma and fluid dynamics and so on. Investigating the exact solutions of BEVC to show the different dynamics of wave phenomena becomes a hot topic both on many mathematicians and physicists. In this paper, by (G′G2)-expansion and the Jacobian elliptic functions (JEFs) two different methods, we found that various forms for exact wave solutions of BEVC. To our best knowledge, we found a variety of new solutions that have not been studied in previous articles such as u13,u14,u511,u512,u513,u514. The most important thing is that there are double Jacobian elliptic functions ideas in finding solution process, which has not been seen before in seeking for nonlinear BEVC. These new exact soliton solutions contain variable coefficients derived in the form of trigonometric function, rational function, and Jacobian elliptic function, hyperbolic function. The obtained results showed many different types such as annihilation, parabolic kink, curved shaped kink, tine shaped, shock solitons and so on. Furthermore, the above obtained solutions for Burgers equation with variable coefficients are different from Mohanty et al. (2022), Zayed and Abdelaziz (2010).
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