The Study On Exact Solution Of Nonlinear Schr(o|¨)dinger Equations

As plasma theory, fluid mechanics and nonlinear optical and other naturalphenomena can be described with mathematical model the nonlinear evolutionequations. Now many effective methods for solving nonlinear evolution equationshave been constructed by some scholars. The exact solutions of nonlinear evolutionequations can reasonable explain the basic rule of natural phenomena. Also the basicrules for predicting the changes in natural phenomena and solving complexengineering design have a very important application.In recent years, optical soliton in optical fiber communication system in longdistance, large capacity transmission highlights its own advantages, will play a greatrole in the next generation communication technology and commercial aspects.Optical solitons in optical fiber transmission can be reasonally described through thenonlinear Schrodinger equation. At present, the solution of the nonlinear Schrodingerequation with two branches, one is the numerical approximation solution, mainly isthe finite element method, finite difference method and spectral method, the second isthe exact solution, mainly is the trial function method, Jacobi elliptic functionexpansion method and trigonometric function assumption.This thesis the research background and the research status of nonlinearSchrodinger equation are introduced; and also the research situation of the solitontheory is discussed.Secondly, the nonlinear Schrodinger equation is derivated by Maxwell equations,and the research results of nonlinear Schrodinger equation are summarized, and thelow constant coefficients of nonlinear Schrodinger equation have been solved by threemethods.Finally, constant coefficients and variable coefficients of the nonlinearSchrodinger equations have been solved through the (G’/G)-expansion method whichwere proposed by Professor Wang Mingliang in2008, and also given an outlook inthe the direction of this research.