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 Schrodinger'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. References: 19
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