Selected Topics in Classical Integrability

Details Selected Topics in Classical Integrability Selected Topics in Classical Integrability

2011-10-19

arxiv.org/abs/1110.4235v3

Int. J. Mod. Phys. A27 (2012) 1230003

Physics

Mathematical Physics

40 pages, Latex. A few typos corrected

Scientific paper

10.1142/S0217751X12300037

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.

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