Optical solitons: Quasi-stationarity versus Lie transform

This paper is a comparitive study of the two approaches namely the quasi-stationarity and the Lie transform that are used for studying the classical optical solitons along with its perturbations governed by the non-linear Schrödinger's equation with Kerr law of non-linearity. The relative advantages and disadvantages of the two methods are enumerated. The study is conducted with both, Hamiltonian as well as non-Hamiltonian type perturbations.