Equivalence transformations of a generalized fifth-order KdV equation with variable coefficients

By using the infinitesimal method, we firstly obtain the equivalence transformations for a class of generalized fifth-order KdV (gfKdV) equation with variable coefficients. With the application of equivalence transformations, the number of variable coefficients is reduced and the most general form which can be mapped by an equivalence transformation to the constant-coefficient equation is explored. Furthermore, the transformational properties of the gauged subclass are proposed via the direct method. We also construct the transformations that connect the three integrable variable coefficient gfKdV equations obtained before by Painlevé test to their integrable constant-coefficient counterparts.