Study of soliton like solutions in nonlinear waveguide modelled by generalized nonlinear schrodinger equation

Abstract

This thesis is devoted to the extensive investigation of solitary wave or soliton-like solutions for variants of nonlinear Schrödinger equation (NLSE) which are collectively known as generalized NLSE (GNLSE). It addresses a variety of nonlinear systems, including optical fibers, tapered graded-index waveguides, and Bose-Einstein condensates (BECs). Real physical systems possess inhomogeneities originating due to the dissipation, environmental fluctuations, spatial modulations and other forces. In order to consider these factors, it is necessary to add the appropriate distributive terms in NLSE. The thesis begins with the study of the exact localized solutions for the complex cubic-quintic Ginzburg-Landau equation, under the influence of intrapulse Raman scattering, in the form of dark and front solitons. The dark solitons are characterized by a novel type of kink solution, which we shall identify as Lambert W-kink solitons. The effect of model coefficients on the amplitude of Lambert W-kink solitons is reported, enabling us to efficiently control the pulse intensity and thus their subsequent evolution. We also investigated moving front solitons for this model. We illustrate the mechanism to regulate the intensity of these fronts, by carefully adjusting the spectral filtering or gain parameter. We present nonlinear resonant state solutions for higher-order nonlinear Schrödinger equation (HNLSE) with Pöschl-Teller potential. Our primary interest in these Pöschl-Teller resonant states derives from the fact that the free parameter in the Pöschl-Teller potential regulates the intensity of optical pulses in nonlinear media. We have determined the nonlinear chirp associated with these localized solutions which can be efficiently controlled by suitably choosing self-steepening and self-frequency shift parameters. Furthermore, we provide a systematic approach based on the isospectral Hamiltonian technique, which provides us with another effective mechanism for amplifying the intensity of propagating pulses.