Dissertation > Excellent graduate degree dissertation topics show

Researches on the Integrable Systems of the Soliton Equations

Author: YueChao
Tutor: ZhangYuFeng
School: Shandong University of Science and Technology
Course: Applied Mathematics
Keywords: nonlinear evolution hierarchy loop algebra zero-curvature equation Hamiltonian structure multi-component integrable system expanding integrable model
CLC: O175.29
Type: Master's thesis
Year: 2006
Downloads: 72
Quote: 0
Read: Download Dissertation

Abstract


Two topics of the dissertation research about the integrable system of the soliton equations include: the formulation and integrability of the nonlinear evolution hierarchy as well as their expanding integrable systems. In the first chapter, historical origin and some researches of soliton theory together with its research meaning are presented. In the second chapter, firstly, an integrable system possessing bi-Hamiltonian structure is presented by choosing V with spectral potentials by use of the zero-curvature equation U_t—V_x+[U,V]=0 andTu scheme, which reduces to a system similar to the AKNS hierarchy and heat conduction equation; Secondly, a type of (2+1)-dimensional multi-component integrable hierarchy is obtained with the help of a (2+1)-dimensional zero-curvature equation and Tu scheme. As reduction cases, the (2+1)-dimensional multi-component AKNS hierarchy and KN hierarchy are worked out respectively; atlast, a loop algebra (X|~) with 3M dimensions is constructed by using of someproperties of exterior algebra, which is devoted to establishing many isospectral problems. As its application, a multi-component system similar to the BPT hierarchy is obtained. In the third chapter, firstly, new expanding loop algebras of the loop algebras presented in the second chapter are constructed, then three kinds of corresponding expanding integrable models are engendered by employing proper isospectral problems and Tu sheme. Secondly, a 6-dimensional Lie algebra is established with the help of the linear combination of a subalgebra, then the extended integrable model of the muti-component KN hierarchy is presented by use of the generalized isospectral problem and Tu sheme. The simple approach to generate expanding integrable models can be used generally.

Related Dissertations

  1. Investigations on Related Problems of the Integrable Coupling Systems and the Exact Solutions of Nonlinear Differential-Difference Equations,O175.7
  2. Three Generalized Akns Integrable Hierarchies and Some Applications of the (G′/G)-Expansion Method for the Nonlinear Evolution Equations,O175.29
  3. Lie Algebras and Researches of Integrable System,O175.29
  4. Some Studies on Some Types of Expanding Model of the Integrable Systems and Painlevé Analysis of Non-Linear Evolution Equation,O175.29
  5. Exact Solutions of Nonlinear Evolution Equation and Formulation of the Integrable Systems as Well as Its Expanding Integrable System,O175.29
  6. Discrete Integrable Systems and Its Integrable Coupling Systems,O175.29
  7. Researches on the Integrable Systems and Exact Solutions of the Soliton Equations,O175.29
  8. Non-Linear Evolution Equation and Integrable System,O175.29
  9. A Soliton Hierarchy Associated with a Energy-dependent 3×3 Matrix Spectral Problem and Their Hamiltonian Structures,O175
  10. Solving Nonlinear Partial Differential Equation and Integrable System,O175.29
  11. Exact Solutions of the Soliton Equations and Researches on the Integrable Systems,O241.8
  12. Investigations on Related Problems of Integrable Hierarchy,O175.29
  13. On the Limit Behavior and Well-Posedness Problem for a New Class of Shallow Water Wave Equations with Dispersive Term,O175.2
  14. Tau Functions of Drinfeld-Sokolov Hierarchies and Some Relevant Problems,O175.5
  15. Integrable Systems and Solutions to Noniospectral Soliton Equations,O175
  16. Integrable Coupling System and Fractional Hamiltonian Structure of Soliton Equation Hierarchy,O175.2
  17. Three Generalized Akns Integrable Hierarchies and Some Applications of the (G′/G)-Expansion Method for the Nonlinear Evolution Equations,O175.29
  18. Lie Algebras and Researches of Integrable System,O175.29
  19. Some Studies on Some Types of Expanding Model of the Integrable Systems and Painlevé Analysis of Non-Linear Evolution Equation,O175.29
  20. Exact Solutions of Nonlinear Evolution Equation and Formulation of the Integrable Systems as Well as Its Expanding Integrable System,O175.29
  21. Discrete Integrable Systems and Its Integrable Coupling Systems,O175.29
  22. Researches on the Integrable Systems and Exact Solutions of the Soliton Equations,O175.29

CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Nonlinear partial differential equations
© 2012 www.DissertationTopic.Net  Mobile