《李-巴克蘭-達布變換(英文)》提出了無限維動力系統、偏微分方程、數學物理交叉學科尖端領域的處理某些議題的新方法。書中的第一部分著重介紹了第一作者在達布變換和同宿軌道以及建立可積偏微分方程梅爾尼科夫積分方面取得的成果。第二部分則專注第二作者將達布變換套用於物理領域的工作。 《李-巴克蘭-達布變換(英文)》的特點在於第一作者及合作者發展的用達布變換建立可積系統中同宿軌道、梅爾尼科夫積分及梅爾尼科夫向量的嶄新方法。可積系統（也叫孤立子方程）是有限維可積哈密頓系統在無限維的對應物，而上述所說的嶄新方法所展示的是無限維相空間結構。 《李-巴克蘭-達布變換(英文)》可供數學、物理及其他相關學科領域的高年級本科生、研究生及該領域的專家參考。
基本介紹
- 書名：李-巴克蘭-達布變換
- 作者：李沿光 優洛夫 (Artyom Yurov)
- 出版日期：2014年1月1日
- 語種：簡體中文, 英語
- 品牌：高等教育出版社
- 外文名：Lie-Backlund-Darboux Transformations
- 出版社：高等教育出版社
- 頁數：160頁
- 開本：16
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《李-巴克蘭-達布變換(英文)》提出了無限維動力系統、偏微分方程、數學物理交叉學科尖端領域的處理某些議題的新方法。書中的第一部分著重介紹了第一作者在達布變換和同宿軌道以及建立可積偏微分方程梅爾尼科夫積分方面取得的成果。第二部分則專注第二作者將達布變換套用於物理領域的工作。
作者簡介
作者：李沿光 （俄羅斯）優洛夫（Artyom Yurov）
圖書目錄
Chapter 1 Introduction
Chapter 2 A Brief Account on Backlund rlyansformations
2.1 A Warm-Up Approach
2.2 Chen's Method
2.3 Clairin's Method
2.4 Hirota's Bilinear Operator Method
2.5 Wahlquist-Estabrook Procedure
Chapter 3 Nonlinear Schrodinger Equation
3.1 Physical Background
3.2 Lax Pair and Floquet Theory
3.3 Darboux rlyansformations and Homoclinic Orbit
3.4 Linear Instability
3.5 Quadratic Products of Eigenfunctions
3.6 Melnikov Vectors
3.7 Melnikov Integrals
Chapter 4 Sine-Gordon Equation
4.1 Background
4.2 Lax Pair
4.3 Darboux Transformations
4.4 Melnikov Vectors
4.5 Heteroclinic Cycle
4.6 Melnikov Vectors Along the Heteroclinic Cycle
Chapter 5 Heisenberg Ferromagnet Equation
5.1 Background
5.2 Lax Pair
5.3 Darboux Transformations
5.4 Figure Eight Structures Connecting to the Domain Wall
5.5 Floquet Theory
5.6 Melnikov Vectors
5.7 Melnikov Vectors Along the Figure Eight Structures
5.8 A Melnikov Function for Landau-Lifshitz-Gilbert Equation
Chapter 6 Vector Nonlinear Schrodinger Equations
6.1 Physical Background
6.2 Lax Pair
6.3 Linearized Equations
6.4 Homoclinic Orbits and Figure Eight Structures
6.5 A Melnikov Vector
Chapter 7 Derivative Nonlinear Schrodinger Equations
7.1 Physical Background
7.2 Lax Pair
7.3 Darboux Transformations
7.4 Floquet Theory
7.5 Strange Tori
7.6 Whisker of the Strange T2
7.7 Whisker of the Circle
7.8 Diffusion
7.9 Diffusion Along the Strange T2
7.10 Diffusion Along the Whisker of the Circle
Chapter 8 Discrete Nonlinear Schrodinger Equation
8.1 Background
8.2 Hamiltonian Structure
8.3 Lax Pair and Floquet Theory
8.4 Examples of Floquet Spectra
8.5 Melnikov Vectors
8.6 Darboux Transformations
8.7 Homoclinic Orbits and Melnikov Vectors
Chapter 9 Davey-Stewartson Ⅱ Equation
9.1 Background
9.2 Linear Stability
9.3 Lax Pair and Darboux Transformations
9.4 Homoclinic Orbits
9.5 Melnikov Vectors
9.5.1 Melnikov Integrals
9.5.2 An Example
9.6 Extra Comments
Chapter 10 Acoustic Spectral Problem
10.1 Physical Background
10.2 Connection with Linear Schrodinger Operator
10.3 Discrete Symmetries of the Acoustic Problem
……
Chapter 11 SUSY and Spectrum Reconstructions
Chapter 12 Darboux Transformations for Dirac Equation
Chapter 13 Moutard Transformations for the 2D and 3D
Chapter 14 BLP Equation
Chapter 15 Goursat Equation
Chapter 16 Links Among Integrable Systems
Bibliography
Index
Chapter 2 A Brief Account on Backlund rlyansformations
2.1 A Warm-Up Approach
2.2 Chen's Method
2.3 Clairin's Method
2.4 Hirota's Bilinear Operator Method
2.5 Wahlquist-Estabrook Procedure
Chapter 3 Nonlinear Schrodinger Equation
3.1 Physical Background
3.2 Lax Pair and Floquet Theory
3.3 Darboux rlyansformations and Homoclinic Orbit
3.4 Linear Instability
3.5 Quadratic Products of Eigenfunctions
3.6 Melnikov Vectors
3.7 Melnikov Integrals
Chapter 4 Sine-Gordon Equation
4.1 Background
4.2 Lax Pair
4.3 Darboux Transformations
4.4 Melnikov Vectors
4.5 Heteroclinic Cycle
4.6 Melnikov Vectors Along the Heteroclinic Cycle
Chapter 5 Heisenberg Ferromagnet Equation
5.1 Background
5.2 Lax Pair
5.3 Darboux Transformations
5.4 Figure Eight Structures Connecting to the Domain Wall
5.5 Floquet Theory
5.6 Melnikov Vectors
5.7 Melnikov Vectors Along the Figure Eight Structures
5.8 A Melnikov Function for Landau-Lifshitz-Gilbert Equation
Chapter 6 Vector Nonlinear Schrodinger Equations
6.1 Physical Background
6.2 Lax Pair
6.3 Linearized Equations
6.4 Homoclinic Orbits and Figure Eight Structures
6.5 A Melnikov Vector
Chapter 7 Derivative Nonlinear Schrodinger Equations
7.1 Physical Background
7.2 Lax Pair
7.3 Darboux Transformations
7.4 Floquet Theory
7.5 Strange Tori
7.6 Whisker of the Strange T2
7.7 Whisker of the Circle
7.8 Diffusion
7.9 Diffusion Along the Strange T2
7.10 Diffusion Along the Whisker of the Circle
Chapter 8 Discrete Nonlinear Schrodinger Equation
8.1 Background
8.2 Hamiltonian Structure
8.3 Lax Pair and Floquet Theory
8.4 Examples of Floquet Spectra
8.5 Melnikov Vectors
8.6 Darboux Transformations
8.7 Homoclinic Orbits and Melnikov Vectors
Chapter 9 Davey-Stewartson Ⅱ Equation
9.1 Background
9.2 Linear Stability
9.3 Lax Pair and Darboux Transformations
9.4 Homoclinic Orbits
9.5 Melnikov Vectors
9.5.1 Melnikov Integrals
9.5.2 An Example
9.6 Extra Comments
Chapter 10 Acoustic Spectral Problem
10.1 Physical Background
10.2 Connection with Linear Schrodinger Operator
10.3 Discrete Symmetries of the Acoustic Problem
……
Chapter 11 SUSY and Spectrum Reconstructions
Chapter 12 Darboux Transformations for Dirac Equation
Chapter 13 Moutard Transformations for the 2D and 3D
Chapter 14 BLP Equation
Chapter 15 Goursat Equation
Chapter 16 Links Among Integrable Systems
Bibliography
Index
