On the Lie point symmetries of the vector Maxwell equations in non-linear optics

Abstract

The vector Maxwell equations of non-linear optics coupled to a single Lorentz oscillator is analyzed by using Lie symmetries. The symmetry are used to obtain classical similarity solutions of the equations to reduce to ordinary differential equations for the electric field intensity. Also, nth dimensional classification of Lie point symmetry subalgebras are given. Finally we obtain the conservation laws of symmetries.