Study of lambert W kink and solitary wave solutions for wave propagation in nonlinear media

Abstract

This thesis delves into an extensive exploration of solitary wave or soliton-like solutions for the generalized nonlinear Schrödinger equation (GNLSE). It examines various nonlinear systems such as optical fibers, tapered graded-index waveguides, and Bose-Einstein condensates etc. It is required to include the relevant distributive terms in NLSE in order to explore the real physical systems. The thesis begins with the study of the exact localized soliton-like solution for the quadratic-cubic NLSE in presence of higher-order terms driven by an external source. These localized solutions are presented in terms of Lambert W-kink solitons. The solutions are found to be chirped, asymmetric and dark in nature. Variation of various coefficients concerning the external source strength has been studied for competing and non-competing quadratic-cubic nonlinearity. We explore the conditions to lock the phase of propagating wave either in- or out of-phase to the external source. In order to control the wave propagation in the tapered graded-index waveguide, we have further explored the Lambert W-kink solutions, which are chirped, dark, and asymmetric in nature, for variable coefficient quadratic cubic-NLSE (vc-QCNLSE) with Raman effect in the presence of external source. The self-similar solutions have been found using similarity transformation. Furthermore, we have demonstrated the dependence of the intensity of self-similar waves on the amplitude of the width-function, the Raman term, and the external driving strength. Further, we present propagating solitonlike double-kink solitons and dark solitons in the complex cubic-quintic Ginzburg-Landau equation(CQGLE) under the influence of Raman effect. Double-kink solitons are found to be chirped. The amplitude of the chirping can be controlled by varying the spectral filtering or gain dispersion. It is, further, verified that the dark soliton solutions exist only for the cubic model of CGLE. newline