The generalized Cole-Hopf transformation to a general variable coefficient Burgers equation with linear damping term

Abstract A general variable coefficient (gVC) Burgers equation with linear damping term has been investigated by using simplified homogeneous balance (SHB) method. The generalized Cole–Hopf transformation for the gVC Burgers equation with linear damping term has been derived out if the damping coefficient satisfies a certain constraint condition. By means of the generalized Cole–Hopf transformation, the exact solutions of the gVC Burgers equation with the certain damping term have been obtained successfully. Several concrete examples (included (2+1)-dimensional damping Burgers equation) of gVC Burgers equation with the certain damping term are studied, and their corresponding generalized Cole–Hopf transformations as well as their corresponding solutions are all given, respectively.