| abstract | 第4页 |
| Chapter 1 Introduction | 第6-9页 |
| 1.1 Motivation | 第6-7页 |
| 1.2 Literature review | 第7-8页 |
| 1.2.1 History of the question | 第7页 |
| 1.2.2 Modern approaches | 第7-8页 |
| 1.3 Thesis Outline/Organization | 第8-9页 |
| Chapter 2 Classical method of symmetric reduction | 第9-36页 |
| 2.1 One-parameter transformation groups | 第9-25页 |
| 2.1.1 Concept of one-parameter transformation group | 第9-15页 |
| 2.1.2 The tangential field of vectors. Equation Lie | 第15-18页 |
| 2.1.3 Infinitesimal group operator. Invariants of group | 第18-25页 |
| 2.2 Groups,which allow differential equations in partial derivatives | 第25-36页 |
| 2.2.1. Continuation methods | 第25-31页 |
| 2.2.2. Indicial equationas | 第31-36页 |
| Chapter 3 Research of symmetry non-linear wave equation and its use for searching of precise decisions | 第36-48页 |
| 3.1. Use symmetry to searching precise decisions cylindrical-symmetric non-linear wave equation | 第36-43页 |
| 3.2. The cylindrical-symmetric non-linear wave equation | 第43-48页 |
| Chapter 4 Conclusion | 第48-49页 |
| Acknowledgements | 第49-50页 |
| Reference | 第50-53页 |
| Publications | 第53页 |
