| Abstract | 第3-6页 |
| Chapter 1 Background of the Study | 第13-17页 |
| 1.1 Introduction | 第13-15页 |
| 1.2 Objective, methodology, and basic research questions | 第15-17页 |
| Chapter 2 Some Qualitative Research Methods on Nonlinear Wave Equation | 第17-47页 |
| 2.1 Highlights on some research methods of nonlinear wave equation | 第17-30页 |
| 2.1.1 Hirota bilinear method | 第18-21页 |
| 2.1.2 Sub-equation methods | 第21-26页 |
| 2.1.3 Lie symmetry analysis method | 第26-28页 |
| 2.1.4 Inverse scattering method | 第28-30页 |
| 2.2 Basic concepts on dynamical system | 第30-47页 |
| 2.2.1 Dynamical behavior of traveling wave systems | 第31-36页 |
| 2.2.2 Two dimensional integrable Hamiltonian systems | 第36-44页 |
| 2.2.3 Some properties Jacobi Elliptic function | 第44-47页 |
| Chapter 3 Studies on Singular Nonlinear Traveling Wave Systems | 第47-65页 |
| 3.1 Models of higher order derivative nonlinear Schrodinger equation | 第47-56页 |
| 3.2 Zakharov-Kuznetsov equation and its further modified form | 第56-58页 |
| 3.3 A generalized Dullin-Gottwald-Holm equation | 第58-60页 |
| 3.4 Other models of mathematical physics considered | 第60-65页 |
| Chapter 4 Dynamical Behavior and Exact Solution in Invariant Manifold fora Septic Order Derivative Nonlinear Schrodinger Equation | 第65-97页 |
| 4.1 Introduction | 第65-66页 |
| 4.2 Dynamical Behavior of system (4.1.1) when p=2 | 第66-72页 |
| 4.3 Exact parametric representations of traveling wave solutions (p=2) | 第72-85页 |
| 4.4 Bifurcation of phase portraits of system (4.1.1) when p=3 | 第85-87页 |
| 4.5 Some traveling wave solutions of system (4.1.1) when p=3 | 第87-97页 |
| Chapter 5 Exact Solution and Dynamical Behavior of Thirteenth Order Deriva-tive Nonlinear Schrodinger Equation | 第97-117页 |
| 5.1 Introduction | 第97-98页 |
| 5.2 Dynamical Behavior of system (5.1.2) when β ∈R | 第98-101页 |
| 5.3 Parametric representation of exact solutions of system (5.1.2)_(β∈R) | 第101-117页 |
| Chapter 6 Bifurcation and Exact Solution of a Generalized Derivative Non-linear Schrodingers Equation | 第117-131页 |
| 6.1 Introduction | 第117-118页 |
| 6.2 Bifurcations of phase portraits of system (6.1.2)_(γ∈R) | 第118-122页 |
| 6.3 Existence of smooth traveling wave solutions of system (6.1.2)_(γ∈R) | 第122-131页 |
| Chapter 7 Exact Traveling Wave Solutions and Bifurcations of a FurtherModified Zakharov-Kuznetsov Equation | 第131-147页 |
| 7.1 Introduction | 第131-132页 |
| 7.2 Bifurcations of phase portraits of system (7.1.2) when the origin isa saddle point | 第132-135页 |
| 7.3 Parametric representations of exact traveling wave solutions of sys-tem (7.1.2) | 第135-147页 |
| 7.3.1 Explicit parametric representations of the solutions of system(7.1.2) | 第135-141页 |
| 7.3.2 More solutions applying the Fan sub-equation method forZK-equation | 第141-147页 |
| Chapter 8 Existence of Kink and Unbounded Traveling Wave Solutions ofthe Casimir equation for the Ito System | 第147-161页 |
| 8.1 Introduction | 第147-148页 |
| 8.2 Bifurcations of phase portraits for of system (8.1.1)~± | 第148-150页 |
| 8.3 Exact explicit bounded traveling wave solutions of system (8.1.1)_(?) | 第150-158页 |
| 8.4 Existence of kink and unbounded traveling wave solutions | 第158-161页 |
| Chapter 9 Various Exact Solutions and Bifurcations of a Generalized Dullin-Gottwald-Holm Equation with a Power Law Nonlinearity | 第161-191页 |
| 9.1 Introduction | 第161-163页 |
| 9.2 Bifurcation of phase portraits of system (9.1.3) | 第163-166页 |
| 9.3 Existence of smooth and non-smooth traveling wave solutions | 第166-181页 |
| 9.4 Dynamical behavior of system (9.1.4) | 第181-184页 |
| 9.5 Existence of smooth solitary, kink and periodic wave solutions | 第184-191页 |
| Chapter 10 Traveling Wave Solutions of a Generalized K(n,2n,-n) Equations | 第191-219页 |
| 10.1 Introduction | 第191-193页 |
| 10.2 Bifurcations of hase ortraits of (10.1.2)_(n=2,3) | 第193-199页 |
| 10.3 Traveling wave solutions of system (10.1.2)_(n=2) | 第199-208页 |
| 10.4 Some exact explicit parametric representation of system(10.1.2)_(n=3) | 第208-219页 |
| Chapter 11 Main Results and Future Study Direction | 第219-223页 |
| 11.1 Main findings of the study | 第219-222页 |
| 11.2 Future study direction | 第222-223页 |
| Bibliography | 第223-240页 |
| Publications | 第240-241页 |
| Acknowledgement | 第241-242页 |
| Curriculum Vitae | 第242-244页 |
