عنوان

Algebraic Aspects of Integrable Systems

(Number (ISBN

9781461224341

(Number (ISBN

9781461275350

Number

b402896

Title Proper

Algebraic Aspects of Integrable Systems

General Material Designation

[Book]

Other Title Information

In Memory of Irene Dorfman /

First Statement of Responsibility

edited by A. S. Fokas, I. M. Gelfand.

Place of Publication, Distribution, etc.

Boston, MA :

Name of Publisher, Distributor, etc.

Birkhäuser Boston,

Date of Publication, Distribution, etc.

1997.

Series Title

Progress in Nonlinear Differential Equations and Their Applications ;

Volume Designation

26

Text of Note

Complex Billiard Hamiltonian Systems and Nonlinear Waves -- Automorphic Pseudodifferential Operators -- On ?-Functions of Zakharov-Shabat and Other Matrix Hierarchies of Integrable Equations -- On the Hamiltonian Representation of the Associativity Equations -- A Plethora of Integrable Bi-Hamiltonian Equations -- Hamiltonian Structures in Stationary Manifold Coordinates -- Compatibility in Abstract Algebraic Structures -- A Theorem of Bochner, Revisited -- Obstacles to Asymptotic Integrability -- Infinitely-Precise Space-Time Discretizations of the Equation ut + uux = 0 -- Trace Formulas and the Canonical 1-Form -- On Some 'Schwarzian' Equations and their Discrete Analogues -- Poisson Brackets for Integrable Lattice Systems -- On the r-Matrix Structure of the Neumann Systems and its Discretizations -- Multiscale Expansions, Symmetries and the Nonlinear Schrödinger Hierarchy -- On a Laplace Sequence of Nonlinear Integrable Ernst-Type Equations -- Classical and Quantum Nonultralocal Systems on the Lattice.

0

Text of Note

Irene Dorfman died in Moscow on April 6, 1994, shortly after seeing her beautiful book on Dirac structures [I]. The present volume contains a collection of papers aiming at celebrating her outstanding contributions to mathematics. Her most important discoveries are associated with the algebraic structures arising in the study of integrable equations. Most of the articles contained in this volume are in the same spirit. Irene, working as a student of Israel Gel'fand made the fundamental dis covery that integrability is closely related to the existence of bi-Hamiltonian structures [2], [3]. These structures were discovered independently, and al most simultaneously, by Magri [4] (see also [5]). Several papers in this book are based on this remarkable discovery. In particular Fokas, Olver, Rosenau construct large classes on integrable equations using bi-Hamiltonian struc tures, Fordy, Harris derive such structures by considering the restriction of isospectral flows to stationary manifolds and Fuchssteiner discusses similar structures in a rather abstract setting.

International Standard Book Number

9781461275350

Title

Springer eBooks

Algebra.

Differential equations, Partial.

Functional analysis.

Mathematics.

Fokas, A. S.

Gelfand, I. M.

SpringerLink (Online service)

Date of Transaction

20190301073800.0

Electronic name

[Book]

Y