SELECTED TOPICS IN CLASSICAL INTEGRABILITY

2011/10/31 by Anastasia Doikou, ANASTASIA DOIKOU · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1142/s0217751x12300037

published as Int. J. Mod. Phys. A27 (2012) 1230003 · 40 pages, Latex. A few typos corrected

openalex publication_date 2012/02/09 · arxiv created 2012/02/29 · arxiv updated 2012/03/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete and continuum classical integrable models is introduced. Using this framework the associated classical integrals of motion and the corresponding Lax pair are extracted based on algebraic considerations. Our attention is restricted to classical discrete and continuum integrable systems with periodic boundary conditions. Typical examples of discrete (Toda chain, discrete NLS model) and continuum integrable models (NLS, sine–Gordon models and affine Toda field theories) are also discussed.

Citations

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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• Learning Lax Pairs: Revisiting the Classical Paradigm

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