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Classical Integrability

Torrielli, A (2016) Classical Integrability Journal of Physics A: Mathematical and Theoretical, 49.

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We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples (harmonic oscillator, Kepler problem); 3. Algebraic tools: Lax pairs, monodromy and transfer matrices, classical r-matrices and exchange relations, non-ultralocal Poisson brackets, with examples (non-linear Schrodinger model, principal chiral field); 4. Features of classical r-matrices: Belavin-Drinfeld theorems, analyticity properties, and lift of the classical structures to quantum groups; 5. Classical inverse scattering method to solve integrable differential equations: soliton solutions, spectral properties and the Gel'fand-Levitan- Marchenko equation, with examples (KdV equation, Sine-Gordon model).

Item Type: Article
Subjects : Mathematics
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Torrielli, A
Date : 20 July 2016
DOI : 10.1088/1751-8113/49/32/323001
Copyright Disclaimer : This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/1751-8113/49/32/323001.
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 04 Jul 2016 13:41
Last Modified : 20 Jul 2017 02:08

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