Lectures on Integrable Systems / by Jens Hoppe.

Format:

Book

Author/Creator:

Hoppe, Jens, 1956- author.

Series:

Lecture Notes in Physics Monographs ; 10

Language:

English

Subjects (All):

Mathematical physics.

Mathematical analysis.

Theoretical, Mathematical and Computational Physics.

Analysis.

Local Subjects:

Theoretical, Mathematical and Computational Physics.

Analysis.

Physical Description:

1 online resource (VII, 111 p.)

Edition:

1st ed. 1992.

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992.

Language Note:

English

Summary:

Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.

Contents:

The Projection Method of Olshanetsky and Perelomov

Classical Integrability of the Calogero-Moser Systems

Solution of a Quantum Mechanical N-Body Problem

Algebraic Approach to x 2 + ?/x 2 Interactions

Some Hamiltonian Mechanics

The Classical Non-Periodic Toda Lattice

r-Matrices and Yang Baxter Equations

Integrable Systems and gl(?)

Infinite Dimensional Toda Systems

Integrable Field Theories from Poisson Algebras

Generalized Garnier Systems and Membranes

Differential Lax Operators

First Order Differential Matrix Lax Operators and Drinfeld-Sokolov Reduction

Zero Curvature Conditions on W ?, Trigonometrical and Universal Enveloping Algebras

Spectral Transform and Solitons

Higher Dimensional ?-Functions.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references at the end of each chapters.

ISBN:

3-540-47274-6