The High Accurate And Conservative Numerical Scheme For A Coupled Nonlinear Schr(?)dinger Ssytem

It is well known that nonlinear Schr(?)dinger equations play a very important role in the research of areas such as high-energy physics,quanturn mechanics,nonlinear optics,supercon duction and deep ripples,etc.Coupled nonlinear Schr(?)dinger equations can describe danalyse lots of events including Bose-Einstein solidification and transformation of light wave,which make the research about it and its numerical solution more and more important.The objective of this thesis is doing research about Schr(?)dinger equations scheme and its propeties .The structure of this thesis is as follsow:Chapter one gives the present conditions about the main numerical solutions of the coupled nonlinear Schr(?)dinger equations,review the previous results and present the primary lemmas used in this thesis.Chapter twe gives a scheme,which need to solve nonlinear algebraic equations by iterative algorithma at each discrete time step.This scheme can not only conserve the energy and charge of systems,but also prove to be convergent and stable by the energy method and its precision is O ( h 4 +τ2).Chaper three proposes a linearizing conservative finite difference scheme to Coupled Nonlinear Schr(?)dinger equations.This scheme conserves the energy and charge of systems and has convergence and stability.What's more,its precision prove to be O ( h 4 +τ2).A numerical example is given in this thesis,and its test result shows that the cost time of the new scheme is shorter than that of the conservative scheme in chapter two.