The Lagrangian Approach to Nonlinear Wave Propagation

Abstract

The increasing importance of nonlinear phenomena in optics makes it essential that a theoretical framework should be developed having sufficient generality to encompass the full range of nonlinear phenomena under investigation, yet which is sufficently flexible to enable analytical calculation of the basic phenomena to be realistic. Nonlinear optics, by definition, involves nonlinear partial differential equations. In particular, Maxwell’s equations are coupled to a Schrödinger equation via a nonlinear polarisation. The wide range of Hamiltonians which can appear in the Schrödinger equation dictates the generality required of the theoretical methods.