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
 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
 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 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
 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
 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
 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 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
 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 Schrödinger 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 Schrödinger Equations
  16.4 NLS and Toda Lattice
 Bibliography
 Index