Lie-B#cklund-Darboux Transformations 李-巴克蘭-達布變換(英文版)
定 價:49 元
- 作者:李尚光,[俄] 優(yōu)洛夫(Yriov,Artyom) 著
- 出版時間:2014/1/1
- ISBN:9787040390568
- 出 版 社:高等教育出版社
- 中圖法分類:H31
- 頁碼:160
- 紙張:膠版紙
- 版次:1
- 開本:16開
《李-巴克蘭-達布變換》提出了無限維動力系統(tǒng)、偏微分方程、數(shù)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應用于物理領域的工作。
《李-巴克蘭-達布變換》的特點在于第一作者及合作者發(fā)展的用達布變換建立可積系統(tǒng)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?煞e系統(tǒng)(也叫孤立子方程)是有限維可積哈密頓系統(tǒng)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》可供數(shù)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。
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 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