《非線性波方程在不變流形上的精確解和分支（英文）》是2019年科學出版社出版的圖書，作者是Li jibin（李繼彬）。
基本介紹
- 中文名：非線性波方程在不變流形上的精確解和分支（英文）
- 作者：李繼彬
- 出版時間：2019年1月
- 出版社：科學出版社
- 頁數：354 頁
- ISBN：9787030609502
- 定價：178 元
- 開本：16 開
- 裝幀：平裝
內容簡介,目錄,
內容簡介
本書的**個目的是對行波解的分類和對奇異非線性行波方程所產生的峰、周期峰、偽峰和緊子的概念進行更系統的解釋。從奇異攝動理論的動力系統和思想，我們證明周期性峰是行波系統的兩個時間尺度光滑經典解。PeaKon是下限意義下的極限解：（i）在固定參數條件下，Peaon是一類周期性Peaon解的一個極限解；（ii）具有可變參數的Peaon是一個偽Pekon族的限制解。我們注意到，一個可積的非線性偏微分方程（非線性波動方程）的行波系統通常是一個可積的常微分方程組。因此，行波系統的相位軌道引起波函式的輪廓，並且行進系統的不同相位軌道引起波函式的不同輪廓。如果可能的話，這樣的非線性行進系統，因為這些解析解對於理解波函式的性質是有用的。本書的第二個目的是引入動力系統方法尋找更具物理意義的可積系統的精確解。
目錄
Contents
Preface
Chapter 1 Some Shallow Water Wave Equations Which Yield Peakons and Compactons 1
1.1 Shallow water wave equations derived from the governing equations via double asymptotic power series expansions 1
1.2 Dynamics of traveling wave solutions to a new highly nonlinear shallow water wave equation 7
Chapter 2 Classiˉcation of Traveling Wave Solutions of the Singular Nonlinear Wave Equations 13
2.1 Some preliminary knowledge of dynamical systems 13
2.2 Bifurcations of phase portraits of travelling wave equations having singular straight lines 18
2.3 Main theorems to identify the wave proˉles for a singular traveling wave systems of the ˉrst class 23
2.4 Classiˉcation of the proˉles of traveling wave solutions via known phase orbits 28
Chapter 3 Exact Parametric Representations of the Orbits Deˉned by A Polynomial Di.erential Systems 54
3.1 Exact parametric representations of the orbits deˉned by the planar quadratic Hamiltonian systems 54
3.2 Exact parametric representations of the orbits deˉned by the symmetric planar cubic Hamiltonian systems 62
Chapter 4 Bifurcations and Exact Solutions of the Traveling Wave Systems for Dullin-Gottwald-Holm Equation 69
4.1 Bifurcations of phase portraits of systems (4.4) 70
4.2 Classiˉcation of all traveling wave solutions of system (4.4)+ and explicit exact parametric representations of the solutions of system (4:4)+ and (4.6) 72
4.3 Classiˉcation of all traveling wave solutions of system (4.4). and explicit exact parametric representations of the solutions of systems (4.6). and (4.4) 86
Chapter 5 Variform Exact One-Peakon Solutions for Some Singular Nonlinear Traveling Wave Equations of the First Kind 96
5.1 Peakon solutions of the generalized Camassa-Holm equation (5.1) 97
5.2 Peakon solutions of the nonlinear dispersion equation K(m; n) 101
5.3 Peakon solutions of the two-component Hunter-Saxton system (5.3) 104
5.4 Peakon solutions of the two-component Camassa-Holm system (5.4) 107
Chapter 6 Bifurcations and Exact Solutions of A Modulated Equation in A Discrete Nonlinear Electrical Transmission Line 111
6.1 Bifurcations of phase portraits of system (6.14) when f3(á) only has a positive zero 115
6.2 Dynamics and some exact parametric representations of the solutions of system (6.14) when f3(á) only has a positive zero 117
6.3 Bifurcations of phase portraits of system (6.14) when f3(á) has exact two positive zeros 123
6.4 Dynamics and some exact parametric representations of the solutions of system (6.14) when f3(á) has exact two positive zeros 126
Chapter 7 Exact Solutions and Dynamics of the Raman Soliton Model in Nanoscale Optical Waveguides， with Metamaterials， Having Polynomial Law Nonlinearity 129
7.1 Bifurcations of phase portraits of system (7.6) 132
7.2 Exact parametric representations of solutions of system (7.6) when there is only one equilibrium point for ˉ = 1; 2 and ˉ = .2;.3 136
7.3 Exact parametric representations of solutions of system (7.6) when there exist three equilibrium points for a0 ＞ 0; ˉ = 1; 2 147
7.4 Exact parametric representations of solutions of system (7.6) when there exist three equilibrium points for a0 ＞ 0; ˉ = .2;.3 163
7.5 Exact parametric representations of solutions of system (7.6) when there exist three equilibrium points for a0 ＜ 0; ˉ = .3;.2; 1; 2 173
Chapter 8 Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications 178
8.1 Exact solutions and dynamics of the integrable quadratic oscillator with damping 179
8.2 Exact solutions and dynamics of the integrable cubic nonlinear oscillator with damping 184
8.3 Exact traveling wave solutions of the van der Waals normal form (8.1) and the Cha.ee-Infante equation (8.4) 188
Chapter 9 Dynamics of Solutions of Some Travelling Wave Systems Determined by Integrable Li.enard System 191
9.1 The ˉrst integrals of Li.enard equation (9.4) under Chiellini's integrability condition 192
9.2 Dynamics of travelling wave solutions of a integrable generalized damped sine-Gordon equation (9.7) 194
9.3 Dynamics of travelling wave solutions of the integrable Burgers equation with one-side potential interaction (9.8) 199
Chapter 10 Bifurcations and Exact Solutions in A Model of Hydrogen-Bonded-Chains 204
10.1 Bifurcations of phase portraits of system (10.2) 206
10.2 The parametric representations of some orbits deˉned by system (10.2) for ＞ 0; ˉp0 6= 0 208
10.3 The parametric representations of some orbits deˉned by system (10.2) for ＜ 0; ˉp0 6= 0 213
10.4 The parametric representations of some orbits deˉned by system (10.2) for ˉp0 = 0 or ˉ ＜ 0 217
10.5 The parametric representations of some orbits intersecting transversely the singular straight line p = §p0 220
Chapter 11 Exact Solutions in Invariant Manifolds of Some Higher-Order Models Describing Nonlinear Waves 224＜b＜ div=＞
