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Lectures on Integrable Systems [electronic resource] / by Jens Hoppe.

By: Contributor(s): Material type: TextTextSeries: Lecture Notes in Physics Monographs ; 10Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1992Description: VII, 111 p. online resourceContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540472742
Subject(s): Additional physical formats: Printed edition:: No titleDDC classification:
  • 530.1 23
LOC classification:
  • QC19.2-20.85
Online resources:
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.
In: Springer eBooksSummary: 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.
Item type: E-BOOKS
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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.

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.

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The Institute of Mathematical Sciences, Chennai, India