Solitary Wave Solutions and Stability nalysis for Nonlinear Evolution Equation

Abstract

In order to understand nonlinear partial differential equations (NLPDEs), physicists and mathematicians need to study exact solutions. Many NLPDEs such as Korteweg de Vries equation (KdV), Sin-Gordon equation, nonlinear Schr¨odinger equation (NLSE), and other equations possess solitons solutions. A soliton, which arises as a result of dispersion and nonlinearity, is a wave that retain their original features while propagating from one medium to another. The trial equation method proposed by Liu it is an advanced analyt- ical method for finding the exact solution of NLPDE in the study of solitons. Another method complete discrimination system for Polynomial Methods (CDSPM) is a collection of explicit expressions developed with the coefficients of a polynomial that contains real or symbolic variables. Using this method CDSPM, we find both the quasi periodic behaviour and sensitivity of nonlinear equation. Additionally, in a mathematical framework, sensitiv- ity analysis examines to see how modifications to a system’s parameters affect its behavior. This thesis examines nonlinear Kakutani-Matsuuchi (NKM) model of internal gravity waves. The evolution of lengthy internal gravity waves in a stratified fluid medium is meticulously captured by the (1+1)-dimensional NKM model. By using trial approach we explore several solutions, such as SW, rational and Jacobi elliptic function (JEF). The CDSPM technique is utilized to examine quasi-periodic behavior, critical solution conditions, bifurcation behav- ior and sensitivity analysis. We also explores the quasi periodic behaviour and sensitivity analysis of our governing models at various initial values. Key words: Kakutani-Matsuuchi equation; solitons, complete discriminant system; quali- tative behaviour; quasi periodic behaviour; sensitivity analysis.