Soliton equations and Hamiltonian systems / L.A. Dickey.

Format:

Book

Author/Creator:

Dickey, Leonid A.

Series:

Advanced series in mathematical physics ; v. 26.

Advanced series in mathematical physics ; v. 26

Language:

English

Subjects (All):

Solitons.

Hamiltonian systems.

Physical Description:

1 online resource (421 p.)

Edition:

2nd ed.

Place of Publication:

River Edge, NJ : World Scientific, c2003.

Language Note:

English

Summary:

The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also bec

Contents:

Contents ; Preface to the Second Edition ; Introduction to the First Edition ; Chapter 1 Integrable Systems Generated by Linear Differential nth Order Operators ; 1.1 Differential Algebra A ; 1.2 Space of Functionals A ; 1.3 Ring of Pseudodifferential Operators

1.4 Lax Pairs. GD Hierarchies of Equations 1.5 First Integrals (Constants of Motion) ; 1.6 Compatibility of the Equations of a Hierarchy ; 1.7 Soliton Solutions ; 1.8 Resolvent. Adler Mapping ; Chapter 2 Hamiltonian Structures ; 2.1 Finite-Dimensional Case ; 2.2 Hamilton Mapping

2.3 Variational Principles 2.4 Symplectic Form on an Orbit of the Coadjoint Representation of a Lie Group ; 2.5 Purely Algebraic Treatment of the Hamiltonian Structure ; 2.6 Examples ; Chapter 3 Hamiltonian Structure of the GD Hierarchies ; 3.1 Lie Algebra V Dual Space Q1 and Module Q0

3.2 Proof of Theorem 3.1.2 3.3 Poisson Bracket ; 3.4 Reduction to the Submanifold Un-1 = 0 ; 3.5 Variational Derivative of the Resolvent ; 3.6 Hamiltonians of the GD Hierarchies ; 3.7 Theory of the KdV-Hierarchy (n = 2) Independent of the General Case

Chapter 4 Modified KdV and GD. The Kupershmidt-Wilson Theorem 4 1 Miura Transformation. The Kupershmidt-Wilson Theorem ; 4.2 Modified KdV Equation. Backlund Transformations ; 4.3 More on Modified GD Equations ; Chapter 5 The KP Hierarchy ; 5.1 Definition of the KP Hierarchy

5.2 Reduction of the KP Hierarchy to GD

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611934453

9781281934451

1281934453

9789812794512

9812794514

OCLC:

879023409