Equivalence transformations and differential invariants of a generalized nonlinear Schrödinger equation

Abstract

By using the Lie's invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schrödinger equations with variable coefficients. Starting from the equivalence generators we construct the differential invariants of order one. We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schrödinger equations which can be mapped, by means of an equivalence transformation, to the well known cubic Schrödinger equation. We also provide the explicit form of the transformation.