Analytical and Soliton Solutions for Nonlinear Schr dinger Equation

Abstract

A soliton which is also known as the traveling wave solution has a unique property,” the collision of two solitons produce the waves whose permanent structure remain the same”. These wave solutions are very stable and having a key role in the mathematical physics, especially in fiber technology. ”A soliton does not change its amplitude, shape and speed for a long distance in a non-local and nonlinear optical media”. The applications of soliton solutions are also in various branches of physics. The soliton solutions can be calculated by using the different types of nonlinearities. The optical solitons are very important in the study of nonlinear optical fibers. In this thesis firstly, we determine different types of soliton solutions of dimensionless form of Quintic Complex Ginzburg-Landau (CGLQ) equation by using modified extended tanh− function method (METFM) and the extended trial equation method (ETEM). Sec- ondly, we obtain bright, singular and Jacobi elliptic soliton solutions for the time fractional perturbed NLSE (TFPNLSE) by using ETEM with Kerr, power and log law nonlineari- ties. Thirdly, we find the combo and dipole soliton solutions for CGLQ model with differ- ent ansatz methods. Next, we construct different soliton solutions for the paraxial NLSE (PNLSE) in Kerr media by ETEM. Then, we get the bright and dark solitons for non- Kerr law NLSE with third order (3OD) and fourth order (4OD) dispersions by Sine-cosine method (SCM)and Bernoullis equation method (BEM) with nonlinearities. In the last, by using Hirota bilinear method (HBM), we obtain the multiple solitons for the nonlinear Telegraph equation (NLTE) and the nonlinear PHI-four equation (NLPFE).