Abstract:

A direct perturbation method is applied for finding exact solitary-wave solution to the Gardner-Burgers equation. Using a perturbation series the connection of the Gardner-Burgers equation with a pair of Riccati equations is established. It is shown that the exact solution can be obtained from the Cole-Hopf transformation that contains the function, which is the solution of a second-order differential equation with constant coefficients. An exact solution of the generalized Gardner-Burgers equation with fourth-order polynomial in the dependent variable is found.

Keywords: exact solitary-wave solutions, perturbation method, Riccati equation