Propagation of a mixture of modes of a laser beam through a saturable nonlinear medium has been studied using JWKB method and the paraxial ray approximation. Two second order nonlinear coupled differential equations for the beam width parameters resembling equations of coupled nonlinear oscillators of unit mass are obtained. A scalar potential of the system has been formulated whose analysis yields some valuable information like existence of two critical values of the potential within which bound state of the system exists. From the stability analysis it has been found that the stable beam propagation depends on the ratio of intensities of the two modes. A threshold of power is defined. When beam power is above the threshold value the propagation is stationary.

Employing collective variable approach, femtosecond pulse propagation has been investigated in optical fibers using the higher order nonlinear Schrödinger equation. In order to view the pulse dynamics along the propagation distance, variation of different pulse parameters, called collective variables, such as pulse amplitude, width, chirp, pulse center and frequency has been investigated by numerically solving the set of ordinary equations obtained from collective variable approach.

In this paper we have investigated the propagation properties of chirped super Gaussian soliton pulses through semiconductor doped glass fibers which is a dispersive medium with cubic quintic nonlinearity. Using variational principle, the evolution equations of the soliton parameters such as amplitude, temporal width, position of centre, chirp etc. have been derived. The dynamics of these parameters have been analysed. Employing linear stability analysis we have shown that super Gaussian solitons are stable in semiconductor doped glass fibers.

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