Study of Solitary Wave Solutions of Some Nonlinear Evolution Equations

Abstract

We investigate soliton interactions within the framework of the Cubic-Quartic Fokas Lenells equation (CQFL) and Nonlinear Schrdinger Equation (NLSE) by employing the generalised Kudryashov approach (GK), Sine jordan equation approach and the Hirota bilinear method (HBM). Many integrable NLEEs possess the soliton solutions which re tains the speed as well as the shape, even after collision with each other. Several efficient techniques have been introduced in literature for obtaining soliton solutions of NLSEs and NLEEs for last two decades, e.g F-expansion approach and its modification, HBM, Sine-Gordon architectonic, and other approaches. The Hirota bilinear method (HBM) was introduced by Ryogo Hirota in 1970s, for solving integrable systems of PDEs and is still used an efficient mathematical method for studying propagation of wave packets. In this thesis, firstly we study soliton interactions by HBM and GKM of Cubic-Quartic Fokes lenell equation with linear gain or loss and time modulated dispersion. Due to its spatially varying coefficients property it has significance in the field of fluid dynamics, classical and quantum field theories, nonlinear optics and physics etc. The nonlinear Schrodinger equation with AC nonlinearity (NLSE-AC) will be studied with the assis- ¨ tance of GKM and SGE and sort out some new solitons and their interactions for our governing model. In this research , we investigate multiple soliton interactions and other solitary wave solutions (SWS) for a NLSE with AC nonlinearity (NLSE-AC). Due to its high order dispersion term. By controlling the parameters, we will obtain S, V, parabolic and anti parabolic, butterfly, bright and dark shaped solitons. Due to variance in grav itation these solitons play a significant role in lasers, magnetic devices and nonlinear phenomena