New Solitary Wave Solution for Nonlinear Schrodinger Equation

Abstract

A nonsingular and localized wave which propagates without change of velocity and shape is called a solitary wave. A soliton is a solution of NLPDE which has a per manent form and is localized. A solitary traveling wave does not obey superposition principle; it does not disperse. Solitary waves retain its permanent structure even when it collides with other soliton [25]. Soliton has many applications in other fields like engineering and biology. Soliton solutions can be calculated with the help of differ ent nonlinearities. These nonlinearities are Kerr law, power law, parabolic law, dual power law, exponential law etc. In this thesis we will study, the soliton solutions of Lakshmanan-Porsezian-Danial (LPD) model. In order to obtain exact soliton solutions several powerful methods have been proposed. We will use modified trail equation method with Kerr and parabolic law to obtain some hyperbolic and rational function solutions to LPD model. We also find new and more general exact traveling wave solution by using improved G′/G-expansion method with Kerr and parabolic laws of nonlinearities