The Analytical Wave Solutions For Some Class Of The Nonlinear Evolution Equations And Their Stability Analysis

Nonlinear evolution equations(NLEEs)are often used to simulate complex physical phenomena in the real-world.It has numerous applications in the field of physics,biology,optical fiber communication and other fields.In non-linear optical fibers,the optical soliton propagation is a topic of huge present since of the broad applications of ultra-fast signal routing systems and short light pulses in telecommunication.In this thesis,some traditional methods for finding analytical wave solutions of non-linear evolution equations are proposed,such as generalized Recatti mapping technique,F-expansion method,auxiliary equation method and extended modified rational expansion method.We apply these proposed methods on some class of nonlinear partial differential equations for example modified Kawahra equation,Perturbed nonlinear schrodinger equation(NLSE),fourth order NLSE,Resonant NLSE with quadratic cubic non-linearity,Generalized third order NLSE and(2+1)-dimensional Heisenberg Ferromagnetic Spin Chain dynamical model,obtained exact wave solutions in the form of trigonometric,hyperbolic,exponential,rational and Jacobi elliptic functions solutions.Some solutions are presented graphically by assigning the suitable values to the parameters under the given conditions which are helpful to understand the physical phenomena of the complex models.Modulation instability analysis is also used to discuss the qualitative properties of obtained solitons of these models.We obtained novel structures such as dark soliton,bright solition,singular,Kink and anti-Kink solitons by giving suitable values to parameters,which have large applications in different branches of physics and other areas of applied sciences.This thesis has established various new solutions for some class of NLEEs,the achieved results demonstrate that our methods are more efficient,straightforward,and reliable tool to solve nonlinear problems.These proposed methods can also applied on coupled nonlinear wave systems that can arise in mathematical physics and other areas of applied sciences.