1.

Record Nr.

UNINA9910782287503321

Autore

Dickey Leonid A

Titolo

Soliton equations and Hamiltonian systems [[electronic resource] /] / L.A. Dickey

Pubbl/distr/stampa

River Edge, NJ, : World Scientific, c2003

ISBN

1-281-93445-3

9786611934453

981-279-451-4

Edizione

[2nd ed.]

Descrizione fisica

1 online resource (421 p.)

Collana

Advanced series in mathematical physics ; ; v. 26

Disciplina

530.12/4

Soggetti

Solitons

Hamiltonian systems

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

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

Sommario/riassunto

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