《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。

前辅文
Chapter 1 Introduction
Chapter 2 A Brief Account on B?cklund 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
Chapter 3 Nonlinear Schr?dinger 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
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 Schr?dinger 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 Schr?dinger 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
Chapter 8 Discrete Nonlinear Schr?dinger 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 Schr?dinger 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
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
Chapter 12 Darboux Transformations for Dirac Equation
  12.1 Dirac Equation
  12.2 Crum Law
Chapter 13 Moutard Transformations for the 2D and 3D Schr?dinger Equations
  13.1 A 2D Moutard Transformation
  13.2 A 3D 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
Chapter 15 Goursat Equation
  15.1 The Reduction Restriction
  15.2 Binary Darboux Transformations
  15.3 Moutard Transformations for 2D-MKdV Equation
Chapter 16 Links Among Integrable Systems
  16.1 Borisov-Zykov’s Method
  16.2 Higher Dimensional Systems
  16.3 Modified Nonlinear Schr?dinger Equations
  16.4 NLS and Toda Lattice
Bibliography
Index

姓名：Y. Charles Li，单位：University of Missouri

现代数学纵览SMM

本书可供数学、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。