Equivalent transformations and exact solutions to the generalized cylindrical KdV type of equation

Abstract

In this paper, by constructing equivalent transformations (ETs) of the generalized cylindrical KdV (cKdV) types of equations, we transform the variable-coefficient partial differential equations (vc-PDEs) into constant-coefficient PDEs (cc-PDEs) under some conditions. Particularly, the classical cKdV equation is transformed into the classical KdV equation accordingly, then the exact solutions to the vc-PDEs are provided in terms of the ETs. Thus, an effective approach to getting exact solutions to vc-PDEs is presented based on the solutions to cc-PDEs.