On solitary wave solutions for the two-dimensional nonlinear modified Kortweg–de Vries–Burger equation

In this paper, we construct an analytic solution of the nonlinear modified Kortweg–de Vries–Burger equation. By applying a special solution of Cole–Hopf transformation to an ordinary differential equation, we propose a bounded travelling wave solution u(x, y, t) = U(ξ) where ξ = kx + ly − wt, to the two-dimensional nonlinear modified Kortweg–de Vries–Burger equation. We use Jacobian and rational methods to calculate the solitary wave solutions for the two-dimensional modified Kortweg–de Vries–Burger equation.