A Study On The Exact Solution Of The Nonlinear GI Model And The MR Compression Bar Model And Its Dynamic Behavior

It is well known that the Schr(?)dinger equation has a very wide range of applications in the field of quantum mechanics(plasmon physics).The two derivatives of this equation,the nonlinear GI model and the nonlinear MR compression rod model,also have a good application prospect in the field of physics.Under some special conditions,the derivative GI model of nonlinear Schr(?)dinger equation can be transformed into the famous Kaup-Newell equation or Chen-Lee-Liu equation.Also,under some special conditions,the derivative MR model of nonlinear Schr(?)dinger equation can be transformed into the famous shallow water wave model,that is Camassa-Holm equation.In this paper,we combine integral bifurcation method with factorization to solve these two nonlinear models accurately,and further analyze the dynamic behavior of their exact solutions evolving with time.Thus,some nonlinear physical phenomena contained in the model are discussed,and the inherent nature and regularity of the model are explained,which provides theoretical support and data analysis basis for the relevant applied disciplines.In the first chapter,we use the integral bifurcation method and factorization to study the exact traveling wave solutions of the nonlinear GI model,including solitary wave solutions,smooth periodic wave solutions and non-smooth periodic cusp wave solutions,etc.Furthermore,the dynamical behavior of some representative traveling wave solutions with time evolution is discussed.In chapter 2,a series of exact traveling wave solutions,such as peaked soliton solution,blow-up wave solution,periodic wave solution,bright soliton solution and dark soliton solution are studied by using similar methods.In order to intuitively show the dynamic behavior and properties of traveling wave solution,several coordinate figures of some representative exact traveling wave solution which develop with time are drawn by using Maple software.Some nonlinear physical phenomena contained in the model are explained.