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Preprint typeset in JHEP style - HYPER VERSION Student Seminar: Classical and Quantum Integrable Systems Gleb Arutyunov a a Institute for Theoretical Physics and Spinoza Institute, Utrecht University 3508 TD Utrecht, The Netherlands Abstract: The students will be guided through the world of classical and quan- tum integrable systems. Starting from the famous Liouville theorem and finite- dimensional integrable models, the basic aspects of integrability will be studied in- cluding elements of the modern classical and quantum soliton theory, the Riemann- Hilbert factorization problem and the Bethe ansatz. Delivered at Utrecht University, 20 September 2006- 24 January 2007

Student Seminar: Classical and Quantum Integrable Systems4.2.2 Sine-Gordon cnoidal wave and soliton 45 4.3 Zero-curvature representation 47 4.4 Local integrals of motion 49 5. Quantum

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