Dynamical Behavior and Exact Solutions of Nonlinear Travelin
发布时间：2021-12-10 12:11
Nonlinear science is an interdisciplinary subject generated by the permeation of physics,mechanics,mathematics,and computer science,as well as the social sciences,notably in economics and demography.Most physical phenomena in real-world problems are described through nonlinear partial differential equations（are also called mathematical physics equations）involving first order or second order derivatives with respect to time,which play an important role to model a complex physical phenomenon in va...
【文章来源】：浙江师范大学浙江省
【文章页数】：244 页
【学位级别】：博士
【文章目录】：
Abstract
Chapter 1 Background of the Study
1.1 Introduction
1.2 Objective, methodology, and basic research questions
Chapter 2 Some Qualitative Research Methods on Nonlinear Wave Equation
2.1 Highlights on some research methods of nonlinear wave equation
2.1.1 Hirota bilinear method
2.1.2 Sub-equation methods
2.1.3 Lie symmetry analysis method
2.1.4 Inverse scattering method
2.2 Basic concepts on dynamical system
2.2.1 Dynamical behavior of traveling wave systems
2.2.2 Two dimensional integrable Hamiltonian systems
2.2.3 Some properties Jacobi Elliptic function
Chapter 3 Studies on Singular Nonlinear Traveling Wave Systems
3.1 Models of higher order derivative nonlinear Schrodinger equation
3.2 Zakharov-Kuznetsov equation and its further modified form
3.3 A generalized Dullin-Gottwald-Holm equation
3.4 Other models of mathematical physics considered
Chapter 4 Dynamical Behavior and Exact Solution in Invariant Manifold fora Septic Order Derivative Nonlinear Schrodinger Equation
4.1 Introduction
4.2 Dynamical Behavior of system (4.1.1) when p=2
4.3 Exact parametric representations of traveling wave solutions (p=2)
4.4 Bifurcation of phase portraits of system (4.1.1) when p=3
4.5 Some traveling wave solutions of system (4.1.1) when p=3
Chapter 5 Exact Solution and Dynamical Behavior of Thirteenth Order Deriva-tive Nonlinear Schrodinger Equation
5.1 Introduction
5.2 Dynamical Behavior of system (5.1.2) when β ∈R
5.3 Parametric representation of exact solutions of system (5.1.2)_(β∈R)
Chapter 6 Bifurcation and Exact Solution of a Generalized Derivative Non-linear Schrodingers Equation
6.1 Introduction
6.2 Bifurcations of phase portraits of system (6.1.2)_(γ∈R)
6.3 Existence of smooth traveling wave solutions of system (6.1.2)_(γ∈R)
Chapter 7 Exact Traveling Wave Solutions and Bifurcations of a FurtherModified Zakharov-Kuznetsov Equation
7.1 Introduction
7.2 Bifurcations of phase portraits of system (7.1.2) when the origin isa saddle point
7.3 Parametric representations of exact traveling wave solutions of sys-tem (7.1.2)
7.3.1 Explicit parametric representations of the solutions of system(7.1.2)
7.3.2 More solutions applying the Fan sub-equation method forZK-equation
Chapter 8 Existence of Kink and Unbounded Traveling Wave Solutions ofthe Casimir equation for the Ito System
8.1 Introduction
8.2 Bifurcations of phase portraits for of system (8.1.1)~±
8.3 Exact explicit bounded traveling wave solutions of system (8.1.1)_(?)
8.4 Existence of kink and unbounded traveling wave solutions
Chapter 9 Various Exact Solutions and Bifurcations of a Generalized Dullin-Gottwald-Holm Equation with a Power Law Nonlinearity
9.1 Introduction
9.2 Bifurcation of phase portraits of system (9.1.3)
9.3 Existence of smooth and non-smooth traveling wave solutions
9.4 Dynamical behavior of system (9.1.4)
9.5 Existence of smooth solitary, kink and periodic wave solutions
Chapter 10 Traveling Wave Solutions of a Generalized K(n,2n,-n) Equations
10.1 Introduction
10.2 Bifurcations of hase ortraits of (10.1.2)_(n=2,3)
10.3 Traveling wave solutions of system (10.1.2)_(n=2)
10.4 Some exact explicit parametric representation of system(10.1.2)_(n=3)
Chapter 11 Main Results and Future Study Direction
11.1 Main findings of the study
11.2 Future study direction
Bibliography
Publications
Acknowledgement
Curriculum Vitae
【参考文献】：
期刊论文
[1]Solitary Wave Solutions of a Generalized Derivative Nonlinear Schrdinger Equation[J]. WANG Ming-Liang~(1,2) ZHANG Jin-Liang~1 LI Xiang-Zheng~1 Science College,Henan University of Science and Technology,Luoyang 471003,China Department of Mathematics,Lanzhou University,Lanzhou 730000,China. Communications in Theoretical Physics. 2008(07)
[2]An Extended Method for Constructing Travelling Wave Solutions to Nonlinear Partial Differential Equations[J]. JIAO Xiao-Yu;WANG Jin-Huan;ZHANG Hong-Qing Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China. Communications in Theoretical Physics. 2005(09)
[3]A Series of Soliton-like and Double-like Periodic Solutions of a （2+1）-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation[J]. CHEN Yong,~(1,3,4, WANG Qi~(2,4) LI Biao~(2,4) ~1Department of Mathematics,Ningbo University,Ningbo 315211,China ~2Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China ~3Department of Physics,Shanghai Jiao Tong University,Shanghai 200030,China ~4Key Laboratory of Mathematics Mechanization~ the Chinese Academy of Sciences,Beijing 100080,China. Communications in Theoretical Physics. 2004(11)
本文编号：3532605
【文章来源】：浙江师范大学浙江省
【文章页数】：244 页
【学位级别】：博士
【文章目录】：
Abstract
Chapter 1 Background of the Study
1.1 Introduction
1.2 Objective, methodology, and basic research questions
Chapter 2 Some Qualitative Research Methods on Nonlinear Wave Equation
2.1 Highlights on some research methods of nonlinear wave equation
2.1.1 Hirota bilinear method
2.1.2 Sub-equation methods
2.1.3 Lie symmetry analysis method
2.1.4 Inverse scattering method
2.2 Basic concepts on dynamical system
2.2.1 Dynamical behavior of traveling wave systems
2.2.2 Two dimensional integrable Hamiltonian systems
2.2.3 Some properties Jacobi Elliptic function
Chapter 3 Studies on Singular Nonlinear Traveling Wave Systems
3.1 Models of higher order derivative nonlinear Schrodinger equation
3.2 Zakharov-Kuznetsov equation and its further modified form
3.3 A generalized Dullin-Gottwald-Holm equation
3.4 Other models of mathematical physics considered
Chapter 4 Dynamical Behavior and Exact Solution in Invariant Manifold fora Septic Order Derivative Nonlinear Schrodinger Equation
4.1 Introduction
4.2 Dynamical Behavior of system (4.1.1) when p=2
4.3 Exact parametric representations of traveling wave solutions (p=2)
4.4 Bifurcation of phase portraits of system (4.1.1) when p=3
4.5 Some traveling wave solutions of system (4.1.1) when p=3
Chapter 5 Exact Solution and Dynamical Behavior of Thirteenth Order Deriva-tive Nonlinear Schrodinger Equation
5.1 Introduction
5.2 Dynamical Behavior of system (5.1.2) when β ∈R
5.3 Parametric representation of exact solutions of system (5.1.2)_(β∈R)
Chapter 6 Bifurcation and Exact Solution of a Generalized Derivative Non-linear Schrodingers Equation
6.1 Introduction
6.2 Bifurcations of phase portraits of system (6.1.2)_(γ∈R)
6.3 Existence of smooth traveling wave solutions of system (6.1.2)_(γ∈R)
Chapter 7 Exact Traveling Wave Solutions and Bifurcations of a FurtherModified Zakharov-Kuznetsov Equation
7.1 Introduction
7.2 Bifurcations of phase portraits of system (7.1.2) when the origin isa saddle point
7.3 Parametric representations of exact traveling wave solutions of sys-tem (7.1.2)
7.3.1 Explicit parametric representations of the solutions of system(7.1.2)
7.3.2 More solutions applying the Fan sub-equation method forZK-equation
Chapter 8 Existence of Kink and Unbounded Traveling Wave Solutions ofthe Casimir equation for the Ito System
8.1 Introduction
8.2 Bifurcations of phase portraits for of system (8.1.1)~±
8.3 Exact explicit bounded traveling wave solutions of system (8.1.1)_(?)
8.4 Existence of kink and unbounded traveling wave solutions
Chapter 9 Various Exact Solutions and Bifurcations of a Generalized Dullin-Gottwald-Holm Equation with a Power Law Nonlinearity
9.1 Introduction
9.2 Bifurcation of phase portraits of system (9.1.3)
9.3 Existence of smooth and non-smooth traveling wave solutions
9.4 Dynamical behavior of system (9.1.4)
9.5 Existence of smooth solitary, kink and periodic wave solutions
Chapter 10 Traveling Wave Solutions of a Generalized K(n,2n,-n) Equations
10.1 Introduction
10.2 Bifurcations of hase ortraits of (10.1.2)_(n=2,3)
10.3 Traveling wave solutions of system (10.1.2)_(n=2)
10.4 Some exact explicit parametric representation of system(10.1.2)_(n=3)
Chapter 11 Main Results and Future Study Direction
11.1 Main findings of the study
11.2 Future study direction
Bibliography
Publications
Acknowledgement
Curriculum Vitae
【参考文献】：
期刊论文
[1]Solitary Wave Solutions of a Generalized Derivative Nonlinear Schrdinger Equation[J]. WANG Ming-Liang~(1,2) ZHANG Jin-Liang~1 LI Xiang-Zheng~1 Science College,Henan University of Science and Technology,Luoyang 471003,China Department of Mathematics,Lanzhou University,Lanzhou 730000,China. Communications in Theoretical Physics. 2008(07)
[2]An Extended Method for Constructing Travelling Wave Solutions to Nonlinear Partial Differential Equations[J]. JIAO Xiao-Yu;WANG Jin-Huan;ZHANG Hong-Qing Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China. Communications in Theoretical Physics. 2005(09)
[3]A Series of Soliton-like and Double-like Periodic Solutions of a （2+1）-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation[J]. CHEN Yong,~(1,3,4, WANG Qi~(2,4) LI Biao~(2,4) ~1Department of Mathematics,Ningbo University,Ningbo 315211,China ~2Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China ~3Department of Physics,Shanghai Jiao Tong University,Shanghai 200030,China ~4Key Laboratory of Mathematics Mechanization~ the Chinese Academy of Sciences,Beijing 100080,China. Communications in Theoretical Physics. 2004(11)
本文编号：3532605
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