Abstract
We develop a new two-mode Burgers equation. We derive multiple kink solutions for this equation only for specific values of the nonlinearity and dispersion parameters. We also present other generalized solutions, including singular, periodic, and rational solutions, for other values of these parameters. We use the simplified Hirota’s method combined with the Cole–Hopf transformation, numerical methods of tanh/coth method, the tan/cot method, and the rational solutions scheme to conduct this study.
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