Dear Professors, While deriving the modified KdV equation using the reductive perturbation method, I encountered a problem with the first term in the final equation. A third-order perturbation term involving the potential (phi) appears, specifically a time derivative of (phi_(3)) Since this term prevents the equation from taking the standard mKdV form, I would like to eliminate it completely. Is there a particular scaling, stretching of variables, or assumption that I can make in order to remove this term? Or should I impose a certain condition on the coefficients so that this term naturally vanishes? I'd appreciate any guidance on how to deal with this issue. Best regards [ Abdelwahab moustafa ]