Overview

The theory of soliton equations and integrable systems has developed rapidly over the past 20 years with applications in both mechanics and physics. A flood of papers followed a work by Gardner, Green, Kruskal and Mizura about the Korteweg-de Vries equation (KdV) which had seemend to be merely and unassuming equation of mathematical physics describing waves in shallow water.

Full Product Details

Author:   L.A. Dickey
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Volume:   Vol 12
Dimensions:   Width: 15.00cm , Height: 1.80cm , Length: 22.00cm
Weight:   0.431kg
ISBN:  

9789810236847

ISBN 10:   9810236840
Pages:   350
Publication Date:   01 September 1991
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Out of Stock Indefinitely
Availability:   Awaiting stock  

Table of Contents

Integrable systems generated by linear differential nth order operators; Hamiltonian structures; Hamiltonian structures of the KdV-hierarchies; the Kupershmidt-Wilson theorem; the KP-hierarchy; Hamiltonian structure of the KP-hierarchy; Baker function, tau-function; Grassmannian, tau-function and Baker function after Segal and Wilson. Algebraic-geometrical Krichever's solutions; matrix first-order operators; KdV-hierarchies as reductions of matrix hierarchies; stationary equations; stationary equations of the KdV-hierarchy in the narrow sense (n=2); stationary equations of the matrix hierarchy; stationary equations of the KdV-hierarchies; matrix differential operators polynomially depending on a parameter; multi-time Lagrangian and Hamiltonian formalism; further examples and applications.

Reviews

There is a bibliography of 112 items. This book is pedagogically written and is highly recommended for its detailed description of the resolvent method for soliton equations. Mathematical Reviews, 1993 The book of L A Dickey presents one more point of view on the mathematical theory of solitons or, in other words, on the theory of nonlinear partial differential equations ... The series of joint papers of I M Gelfand and L A Dickey in the middle of the seventies was an important step in the development of the mathematical theory of nonlinear integrable equations ... As a whole the book presents a very good exposition of the important part of the soliton theory. Mathematics Abstracts

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