Chirped super-Gaussian and super-sech perturbation of nonlinear Schrödinger equation with quadratic-cubic nonlinearity by variational principle (article tiré d’encadrement de thèse)

Abstract

We apply variational method to the perturbed nonlinear Schrödinger equation having quadratic-cubic form of nonlinearity, to study localized optical pulses. Super-Gaussian and super-sech solitons are used as envelopes for the trial function. Numerical simulations are presented for specific values of the Gaussian and super-sech pulse parameters. The impact of the quadratic-cubic terms on the evolution for different parameters is assessed. In general, when the nonlinear quadratic and cubic coefficients increase, the frequency of the oscillations of the collective variables also increases.