ABSTRACT
This chapter discusses the detailed aspects of optical solitons that are governed by the nonlinear Schroo dinger’s equation (NLSE) with Kerr law nonlinearity, which is also commonly known as the cubic Schroodinger’s equation. It provides an introductory discussion about the technique of inverse scattering transform that is used to integrate the NLSE with Kerr law nonlinearity. The chapter presents the Lie transform technique that can be used to integrate the perturbed NLSE, for Kerr law, that contains Hamiltonian perturbation terms only. The Kerr law of nonlinearity originates from the fact that a light wave in an optical fiber faces nonlinear responses from nonharmonic motion of electrons bound in molecules, caused by an external electric field. An important property of the NLSE with the Kerr law of nonlinearity is that it has an infinite number of integrals of motion.
