Generalized Dodd-Bullough-Mikhailov equations with given classes of solutions

Abstract The paper refers to a special approach within the framework of the auxiliary equations method for solving nonlinear differential equations. The focus is on identifying a generalized class of equations that remain consistent with a fixed form of solutions accepted by a specific equation. In particular, we explore the generalization of the DBM equation by examining possible extensions of the derivative-free term. The objective is to extend the equation in a manner that preserves the solutions of the standard equation, thereby offering new insights into the broader applicability of these solutions within nonlinear differential systems.