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图书目录
Lie-Bäcklund-Darboux Transformations 李-巴克兰-达布变换（英文版）
《李-巴克兰-达布变换》提出了无限维动力系统、偏微分方程、数学物理交叉学科尖端领域的处理某些议题的新方法。书中的第一部分着重介绍了第一作者在达布变换和同宿轨道以及建立可积偏微分方程梅尔尼科夫积分方面取得的成果。第二部分则专注第二作者将达布变换应用于物理领域的工作。
《李-巴克兰-达布变换》的特点在于第一作者及合作者发展的用达布变换建立可积系统中同宿轨道、梅尔尼科夫积分及梅尔尼科夫向量的崭新方法。可积系统（也叫孤立子方程）是有限维可积哈密顿系统在无限维的对应物，而上述所说的崭新方法所展示的是无限维相空间结构。
《李-巴克兰-达布变换》可供数学、物理及其他相关学科领域的高年级本科生、研究生及该领域的专家参考。
作者：
Y. Charles Li, Artyom Yurov
定价：
49.00 元
出版时间：
2014-01-29
ISBN：
978-7-04-039056-8
物料号：
39056-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
动力系统
重点项目：
暂无
版面字数：
200千字
开本：
16开
装帧形式：
精装
页数：
161
最新印次时间：
2014年01月
- 目录
- 前辅文
- Chapter 1 Introduction
- Chapter 2 A Brief Account on Bäcklund Transformations
- 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
- 2.1 A Warm-Up Approach
- Chapter 3 Nonlinear Schrödinger Equation
- 3.1 Physical Background
- 3.2 Lax Pair and Floquet Theory
- 3.3 Darboux Transformations and Homoclinic Orbit
- 3.4 Linear Instability
- 3.5 Quadratic Products of Eigenfunctions
- 3.6 Melnikov Vectors
- 3.7 Melnikov Integrals
- 3.1 Physical Background
- 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
- 4.1 Background
- 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
- 5.1 Background
- Chapter 6 Vector Nonlinear Schrödinger 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
- 6.1 Physical Background
- Chapter 7 Derivative Nonlinear Schrödinger 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 T
- 7.7 Whisker of the Circle
- 7.8 Diffusion
- 7.9 Diffusion Along the Strange T
- 7.10 Diffusion Along the Whisker of the Circle
- 7.1 Physical Background
- Chapter 8 Discrete Nonlinear Schrödinger 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
- 8.1 Background
- 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
- 9.1 Background
- Chapter 10 Acoustic Spectral Problem
- 10.1 Physical Background
- 10.2 Connection with Linear Schrödinger Operator
- 10.3 Discrete Symmetries of the Acoustic Problem
- 10.4 Crum Formulae and Dressing Chains for the Acoustic Problem
- 10.5 Harry-Dym Equation
- 10.6 Modified Harry-Dym Equation
- 10.7 Moutard Transformations
- 10.1 Physical Background
- Chapter 11 SUSY and Spectrum Reconstructions
- 11.1 SUSY in Two Dimensions
- 11.2 The Level Addition
- 11.3 Potentials with Cylindrical Symmetry
- 11.4 Extended Supersymmetry
- 11.1 SUSY in Two Dimensions
- Chapter 12 Darboux Transformations for Dirac Equation
- 12.1 Dirac Equation
- 12.2 Crum Law
- 12.1 Dirac Equation
- Chapter 13 Moutard Transformations for the 2D and 3D Schrödinger Equations
- 13.1 A 2D Moutard Transformation
- 13.2 A 3D Moutard Transformation
- 13.1 A 2D Moutard Transformation
- Chapter 14 BLP Equation
- 14.1 The Darboux Transformations for the BLP Equation
- 14.2 Crum Law
- 14.3 Exact Solutions
- 14.4 Dressing From Burgers Equation
- 14.1 The Darboux Transformations for the BLP Equation
- Chapter 15 Goursat Equation
- 15.1 The Reduction Restriction
- 15.2 Binary Darboux Transformations
- 15.3 Moutard Transformations for 2D-MKdV Equation
- 15.1 The Reduction Restriction
- Chapter 16 Links Among Integrable Systems
- 16.1 Borisov-Zykov’s Method
- 16.2 Higher Dimensional Systems
- 16.3 Modified Nonlinear Schrödinger Equations
- 16.4 NLS and Toda Lattice
- 16.1 Borisov-Zykov’s Method
- Bibliography
- Index
- 前辅文
