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The multiple-scale perturbation analysis is used to study the perturbed nonlinear Schrödinger equation, due to power law nonlinearity, that governs the propagation of solitons through an optical fibre. We have considered the perturbations due to the nonlinear damping and saturable amplifiers. A new definition of the phase of the soliton is introduced that captures the corrections to the pulse where the standard soliton perturbation theory fails. The numerical results support the analysis.
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Anjan Biswas (2003) studied this question.
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