Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

By using the approximate derivative-dependent functional variable separation approach,we study the quasi-linear diffusion equations with a weak source u t=(A(u)u x)x+ B(u,u x).A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed.As a consequence,some approximate solutions to the resulting perturbed equations are constructed via examples.