Phys-495: Integrable Models

Description

Outline

  1. 21.10.2020
    • Introduction to the course

Project

Projects will involve studying a paper of interest, writing a 5 – (infinity) page report and making a brief oral online presentation (30 – 45 minutes) at the end of the course.

  1. Fifty years of the finite nonperiodic Toda lattice: a geometric and topological viewpoint, Yuji Kodama and Barbara A Shipman, 2018 J. Phys. A: Math. Theor. 51 353001 [link] (Dilara Kosva)
  2. Kovalevskaya Top: An Elementary Approach, A. M. Perelomov, Theoretical and Mathematical Physics volume 131, pages 612–620 (2002) [link] (Ege Çoban)
  3. Korteweg‐de Vries equation and generalizations. IV. The Korteweg‐de Vries equation as a Hamiltonian system, C.S. Gardner, Journal of Mathematical Physics 12, 1548 (1971) [link] (Oğuz Öner)
  4. Integrable lattices, V. G. Marikhin & A. B. Shabat Theoretical and Mathematical Physics volume 118, pages 173–182 (1999) [link] (Mehmet Dede)
  5. First integrals of generalized Toda chains, V. É. Adler & A. B. Shabat Theoretical and Mathematical Physics volume 115, pages 639–646 (1998) [link]
  6. Dressing the Dressing Chain, Charalampos A. Evripidou, Peter H. van der Kamp, Cheng Zhang, SIGMA, 14 (2018), 059, 14 pp [link] (Osman Ergeç)
  7. Action as an invariant of Bäcklund transformations for Lagrangian systems, V. G. Marikhin Theoretical and Mathematical Physics volume 184, pages 953–960 (2015) [link]
  8. The structure of polynomial conservation laws, R. N. Garifullin & A. B. Shabat Theoretical and Mathematical Physics volume 161, pages 1590–1598 (2009) [link] (Nuri Taş)
  9. An introduction to Lax pairs and the zero curvature representation, Govind S. Krishnaswami, T. R. Vishnu, arXiv:2004.05791 (Özgür Aydın)
  10. Hamiltonian formulation of the KdV equation, Yavuz Nutku, Journal of Mathematical Physics 25, 2007 (1984) [link] (Ali Pazarcı)
  11. The Ruijsenaars-Schneider Model Harry W. Braden, Ryu Sasaki, Prog.Theor.Phys.97:1003-1018,1997, arXiv:hep-th/9702182 (Mehmet Batu Bayındırlı)
  12. A systematic construction of completely integrable Hamiltonians from coalgebras, Angel Ballesteros and Orlando Ragnisco, Journal of Physics A: Mathematical and General, Volume 31, Number 16a (1998) [link] (Mert Akdenizli)
  13. Integrable systems and the topology of isospectral manifolds, A. V. Penskoi Theoretical and Mathematical Physics volume 155, pages 627–632 (2008) [link] (Ege Aktener)
  14. A new goldfish model, F. Calogero Theoretical and Mathematical Physics volume 167, pages 714–724 (2011) [link]

Literature

  • Olivier Babelon, Denis Bernard and Michel Talon, Introduction to Classical Integrable Systems, Cambridge Monographs on Mathematical Physics
  • O. Babelon, A Short Introduction to Classical and Quantum Integrable Systems, lecture notes

Participants

  1. Özgür Aydın
  2. Mustafa Türe
  3. Murat Önem
  4. Birtan Ilkan
  5. Taha Ayfer
  6. Dilara Kosva
  7. Mehmet Batu Bayındırlı
  8. Oğuz Öner
  9. Ege Aktener
  10. Ege Çoban
  11. Şebnem Karaçubuk
  12. Mert Akdenizli
  13. Mehmet Dede
  14. Ali Pazarcı
  15. Deniz Bozkurt
  16. Osman Ergec
  17. Nuri Taş
  18. Mehmet Velat İnci