Two-mode coupled Burgers equation: Multiple-kink solutions and other exact solutions

In this paper, we establish a new two-mode coupled Burgers equation (TMCBE). The necessary conditions that make the multiple kink solutions and the multiple singular kink solutions to TMCBE exist are founded using the simplified bilinear method. Moreover, we find other exact solutions using the hyperbolic-expansion method such as the sech-csch method, the tanh-coth method, and the sinh-cosh method to conduct this study. Finally, this coupled is new and all results obtained didn?t exist in any other work prior to this paper.