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1、宁波大学硕士学位论文孤子方程的数值解和混沌系统的函数级联同步姓名：安红利申请学位级别：硕士专业：基础数学指导教师：陈勇20080428?,?.?.?,?,? ?.?.?,?.?:?:?-?(?)?,?(?)?.?Maple?,?Adomian?,?,?(?);?,?,?,?.?; Adomian?;?,?.?Adomian?.?:?,?;?,?;?KdV?,?positon?negaton?complexiton?.?,?Lorenz?L u?H enon?,?.?.?:?,?, Adomian?,?,?, Complexiton?,?,?.I?Numerical Solutions of S
2、oliton Equation and Function Cascade Synchronization of Chaotic SystemAbstractWith the development of science and technology, nonlinear science has developed rapidlyand involved in almost all the scientific fields. Chaos?soliton and fractal consist of the mainthree branches of nonlinear science. The
3、re are many theoretical significance and applicable valueto investigate them, such as optical soliton communication, chaos secure communication and thelength of the coastline et al.This dissertation investigates two problems of numerical solutions of soliton equations andchaos synchronization. Altho
4、ugh different with each other, in fact, they have many commoncharacteristics. For example, both of them are relevant to nonlinear system: soliton is associatedwith nonlinear partial differential?ordinary differential?differential-integral equation (system)et al and chaos relevant with nonlinear ordi
5、nary differential?difference one (ones) et al.In this dissertation, based on symbolic-numeric computation software, the applications ofAdomian decomposition method and homotopy perturbation method are extended to a numberof nonlinear soliton equations owning important physical significance and some
6、useful generalnumerical (approximate) solutions are obtained. The chaos synchronization is also further in-vestigated: the function cascade synchronization method is proposed for both continuous-timeand discrete-time systems and its automatic reasoning scheme is given; the function cascadesynchroniz
7、ation is realized for some chaotic systems including continuous?discrete?with andwithout unknown parameters systems.It is organized as follows:Chapter 1 briefly reviews the history and progress of soliton, Adomian decompositionmethod, homoptopy perturbation method as well as chaos and chaos synchron
8、ization. Someachievements on these subjects involved in this dissertation are presented at home and abroad.Chapter 2 directly extends the Adomian decomposition method and homotopy perturbationmethod to study some nonlinear soliton equations with physical significance. These two methodswere used for
9、differential equations of integer order traditionally. We investigate and obtain somegeneral numerical solutions of the nonlinear evolution equations with nonlinear terms of anyorder; a type of nonlinear fractional coupled differential equations and some numerical solutionsowning actual physical mea
10、ning; the complex KdV equation and the numerical positon?negatonsolutions as well as numerical complexiton solutions.Chapter 3 gives the automatic reasoning scheme of the function cascade synchronizationmethod for both continuous-time and discrete-time chaotic system. The function cascade syn-III?ch
11、ronization of chaotic system is investigated, which includes the unified chaotic system?Lorenzsystem with unknown parameters?hyperchaotic L u system?discrete-time generalized H enonmap and so on.Numerical simulations are used to verify the effectiveness of the proposedscheme.Chapter 4 is the summary
12、 and outlook of the dissertation.Key Words: Soliton theory, Nonlinear equations, Adomian decomposition method, Homotopyperturbation method, Numerical solution, Chaos synchronization, Function cascade synchro-nization method.IV?:? ?.?,?,?,?.?.?:?:?,?:?,?;?,?.(?.)?:?:?:?Adomian?,?.1.1?1.1.1?1834?.?,?Russell?1.?1844?14?10?2.?60?1895?,?Korteweg?de Vries?,? ?,?KdV?3,?,?,?.?.?,?:?
