| 摘要 | 第8-9页 |
| Abstract | 第9-10页 |
| Introduction | 第11-18页 |
| Chapter 1 Preliminaries | 第18-25页 |
| 1.1 Discrete gradient methods | 第18-20页 |
| 1.2 Average vector field method | 第20-23页 |
| 1.2.1 AVF method for ODEs with energy conservation | 第21-22页 |
| 1.2.2 AVF method for ADEs with energy conservation | 第22-23页 |
| 1.3 Multi-symplectic Hamiltonian PDEs | 第23页 |
| 1.4 Some notations | 第23-25页 |
| Chapter 2 Multi-symplectic Fourier pseudospectral method for the Kawa-hara equation | 第25-47页 |
| 2.1 Multi-symplectic formulation of the Kawahara equation | 第26-27页 |
| 2.2 The relationship between the SDM and DFT | 第27-30页 |
| 2.3 The MSFP method for the Kawahara equation | 第30-35页 |
| 2.4 Numerical Results | 第35-46页 |
| 2.4.1 Solitary Waves | 第35-42页 |
| 2.4.2 Oscillatory Solitary Waves | 第42-46页 |
| 2.5 Conclusions | 第46-47页 |
| Chapter 3 Energy-preserving wavelet collocation method for general multi-symplectic formulations of Hamiltonian PDEs | 第47-74页 |
| 3.1 EPWCM for multi-symplectic Hamiltonian system | 第48-53页 |
| 3.1.1 Autocorrelation functions | 第48-49页 |
| 3.1.2 EPWCM for multi-symplectic PDEs | 第49-53页 |
| 3.2 EPWCM for the NLS equation | 第53-55页 |
| 3.3 EPWCM for the CH equation | 第55-59页 |
| 3.4 Numerical simulation for the NLS equation | 第59-64页 |
| 3.5 Numerical simulation for the CH equation | 第64-73页 |
| 3.6 Conclusions | 第73-74页 |
| Chapter 4 Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs | 第74-106页 |
| 4.1 Structure-preserving algorithms for multi-symplectic PDEs | 第75-85页 |
| 4.1.1 LEP algorithm for multi-symplectic PDEs | 第75-78页 |
| 4.1.2 GEP methods for multi-symplectic PDEs | 第78-83页 |
| 4.1.3 LMP algorithm for multi-symplectic PDEs | 第83-85页 |
| 4.2 Structure-preserving algorithms for the NLS equation | 第85-87页 |
| 4.3 Structure-preserving algorithms for the KdV equation | 第87-90页 |
| 4.4 Numerical experiments | 第90-105页 |
| 4.4.1 Numerical simulation for the NLS equation | 第90-101页 |
| 4.4.2 Numerical simulation for the KdV equation | 第101-105页 |
| 4.5 Concluding remarks | 第105-106页 |
| Chapter 5 Analysis of a new conservative Fourier pseudospectral algo-rithm for the coupled nonlinear Schrodinger equations | 第106-137页 |
| 5.1 Construction of conservative algorithm | 第108-115页 |
| 5.2 Existence,uniqueness and stability of the scheme | 第115-121页 |
| 5.3 Convergence analysis of the scheme | 第121-127页 |
| 5.4 Numerical experiments | 第127-136页 |
| 5.4.1 Single soliton | 第127-130页 |
| 5.4.2 Collision of two solitons | 第130-136页 |
| 5.5 Conclusions | 第136-137页 |
| Bibliography | 第137-148页 |
| Publications and Finished Papers | 第148-149页 |
| Acknowledgements | 第149页 |
