法德维编著的《孤立子理论中的哈密顿方法》旨在讲述逆散射方法及其在孤立子中的应用—哈密顿方法。前半部分讲述非线性Schrodinger方程；后半部分介绍sine-Gordon方程和Heisenberg方程，以及构成他们解的可积模型和方法的分类。目次：（一）非线性Schrodinger方程：零曲率表示；黎曼问题；哈密尔顿公式；（二）可积发展问题方程的一般理论：基本例子及其一般性质；基础连续模型；可积模型分类和分析的李代数方法。读者对象：数学物理、力学专业的研究生和相关的科研人员。

Introduction References

Part One The Nonlinear Schrodinger Equation (NS Model)

Chapter Ⅰ Zero Curvature Representation

1.Formulation of the NS Model

2.Zero Curvature Condition

3.Properties of the Monodromy Matrix in the Quasi-Periodic Case

4.Local Integrals of the Motion

5.The Monodromy Matrix in the Rapidly Decreasing Case

6.Analytic Properties of Transition Coefficients

7.The Dynamics of Transition Coefficients

8.The Case of Finite Density.Jost Solutions

9.The Case of Finite Density.Transition Coefficients

10.The Case of Finite Density.Time Dynamics and Integrals of the Motion

1.Notes and References

References

Chapter Ⅱ The Riemann Problem

1.The Rapidly Decreasing Case.Formulation of the Riemann Problem

2.The Rapidly Decreasing Case.Analysis of the Riemann Problem

3.Application of the Inverse Scattering Problem to the NS Model

4.Relationship Between the Riemann Problem Method and the Gelfand-Levitan-Marchenko Integral Equations Formulation

5.The Rapidly Decreasing Case.Soliton Solutions

6.Solution of the Inverse Problem in the Case of Finite Density.The Riemann Problem Method

7.Solution of the Inverse Problem in the Case of Finite Density.The Gelfand-Levitan-Marchenko Formulation

8.Soliton Solutions in the Case of Finite Density

9.Notes and References References

Chapter Ⅲ The Hamiltonian Formulation

1.Fundamental Poisson Brackets and the /"-Matrix

2.Poisson Commutativity of the Motion Integrals in the Quasi-Periodic Case

3.Derivation of the Zero Curvature Representation from the Fundamental Poisson Brackets

4.Integrals of the Motion in the Rapidly Decreasing Case and in the Case of Finite Density

5.The A-Operator and a Hierarchy of Poisson Structures

6.Poisson Brackets of Transition Coefficients in the Rapidly Decreasing Case

7.Action-Angle Variables in the Rapidly Decreasing Case

8.Soliton Dynamics from the Hamiltonian Point of View

9.Complete Integrability in the Case of Finite Density

10.Notes and References

References

Part Two General Theory of Integrable Evolution Equations

Chapter Ⅰ Basic Examples and Their General Properties

1.Formulation of the Basic Continuous Models

2.Examples of Lattice Models

3.Zero Curvature Representation's a Method for Constructing Integrable Equations

4.Gauge Equivalence of the NS Model (#=-1) and the HM Model

5.Hamiltonian Formulation of the Chiral Field Equations and Related Models

6.The Riemann Problem as a Method for Constructing Solutions of Integrable Equations

7.A Scheme for Constructing the General Solution of the Zero Curvature Equation. Concluding Remarks on Integrable Equations

8.Notes and References

References

Chapter Ⅱ Fundamental Continuous Models

1.The Auxiliary Linear Problem for the HM Model

2.The Inverse Problem for the HM Model

3.Hamiltonian Formulation of the HM Model 4.The Auxiliary Linear Problem for the SG Model

5.The Inverse Problem for the SG Model

6.Hamiltonian Formulation of the SG Model

7.The SG Model in Light-Cone Coordinates

8.The Landau-Lifshitz Equation as a Universal Integrable Model with Two-Dimensional Auxiliary Space

9.Notes and References

References

Chapter III.Fundamental Models on the Lattice

1.Complete Integrability of the Toda Model in the Quasi-Peri-odic Case

2.The Auxiliary Linear Problem for the Toda Model in the Rap-idly Decreasing Case

3.The Inverse Problem and Soliton Dynamics for the Toda Model in the Rapidly Decreasing Case

4.Complete Integrability of the Toda Model in the Rapidly Decreasing Case

5.The Lattice LL Model as a Universal'Integrable System with Two-Dimensional Auxiliary Space

6.Notes and References

References

Chapter IV.Lie-Algebraic Approach to the Classification and Analysis

of Integrable Models

1.Fundamental Poisson Brackets Generated by the Current Algebra

2.Trigonometric and Elliptic r-Matrices and the Related Fundamental Poisson Brackets

3.Fundamental Poisson Brackets on the Lattice

4.Geometric Interpretation of the Zero Curvature Representation and the Riemann Problem Method

5.The General Scheme as Illustrated with the NS Model

6.Notes and References

References

Conclusion

List of Symbols

Index