A simple direct method to find equivalence transformations of a generalized nonlinear Schrödinger equation and a generalized KdV equation

Abstract

A simple direct method is presented to find equivalence transformations of nonlinear mathematical physics equations. By using the direct method, we obtain the continuous equivalence transformations of a class of nonlinear Schröequations with variable coefficients and a family of nonlinear KdV equations with variable coefficients. For the nonlinear Schrödinger equations with variable coefficients, the equivalence transformations obtained by the direct method coincide, in nature, with those obtained via the infinitesimal Lie criterion, but our computation is much simpler.