an:04028446
Zbl 0632.58003
Takhtadzhyan, L. A.; Faddeev, L. D.
Hamiltonian methods in the theory of solitons.
RU
Moskva: ``Nauka''. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 528 p. R. 3.00 (GOE 87 A 25546) (1986).
1986
b
37-02 37J35 37K10 37K15 37K40 37K30 37K60 81Q05 81U40 58J50 35Q51 35Q55 35Q58
Hamiltonian systems; inverse scattering; nonlinear Schrödinger equation; sine-Gordon equation; Heisenberg equation; Toda lattice; Riemann problem; evolution equations; integrable models
The book gives the exposition of the inverse scattering method and its application to soliton theory. It deals with the classical part of the subject only; the authors are planning to write a second volume devoted to quantum aspects. The main characteristic feature of this book is the consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation (not the KdV equation as usual) is considered as a main example; the investigation of this equation forms the first part of the book. The second part is devoted to such fundamental models as the sine-Gordon equation, Heisenberg equation, Toda lattice, etc., the classification of integrable models and the methods for constructing their solutions.
The following list of chapters gives more details as to the contents: Part I. Nonlinear Schrödinger equation. Chapter 1. Representation of zero curvature. Chapter 2. Riemann problem. Chapter 3. Hamiltonian formulation.
Part II. General theory of integrable evolution equations. Chapter 1. Main examples and their general properties. Chapter 2. Fundamental continuous models. Chapter 3. Fundamental models on a lattice. Chapter 4. Lie-algebraic approach to the classification and investigation of integrable models.
Yu.E.Glikhlikh
0632.58004