Advanced search
Publication Cover
Journal of Nonlinear Mathematical Physics Volume 26, 2019 - Issue 4
Journal homepage
56
Views
0
CrossRef citations to date
0
Altmetric
Articles

Constructing discrete Painlevé equations: from E8(1) to A1(1) and back

A. RamaniIMNC, CNRS, Université Paris-Diderot, Université Paris-Sud, Université Paris-Saclay, 91405Orsay, France
,
B. GrammaticosIMNC, CNRS, Université Paris-Diderot, Université Paris-Sud, Université Paris-Saclay, 91405Orsay, France
,
R. WilloxGraduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8914Tokyo, Japan
&
T. TamizhmaniSAS, Vellore Institute of Technology, Vellore - 632014, Tamil Nadu, India
Pages 520-535 | Received 20 Feb 2019, Accepted 21 Apr 2019, Published online: 09 Jul 2019

References

  • H. Sakai, Commun. Math. Phys. 220 (2001) 165. doi: 10.1007/s002200100446
  • Y. Ohta, A. Ramani and B. Grammaticos, J. Phys. A 35 (2002) L653. doi: 10.1088/0305-4470/35/45/104
  • Y. Ohta, A. Ramani and B. Grammaticos, J. Phys. A 34 (2001) 10523. doi: 10.1088/0305-4470/34/48/316
  • B. Grammaticos and A. Ramani, J. Phys. A 48 (2015) 16FT02. doi: 10.1088/1751-8113/48/16/16FT02
  • B. Grammaticos and A. Ramani, J. Math. Phys. 56 (2015) 083507. doi: 10.1063/1.4927341
  • A. Ramani and B. Grammaticos, J. Phys. A 48 (2015) 355204. doi: 10.1088/1751-8113/48/35/355204
  • B. Grammaticos, A. Ramani and R. Willox, Restoring discrete Painlevé associated one, preprint (2018), arXiv:1812.00712 [math-ph].
  • G.R.W. Quispel, J.A.G. Roberts and C.J. Thompson, Physica D 34 (1989) 183. doi: 10.1016/0167-2789(89)90233-9
  • A. Ramani, S. Carstea, B. Grammaticos and Y. Ohta, Physica A 305 (2002) 437. doi: 10.1016/S0378-4371(01)00619-7
  • A. Ramani, B. Grammaticos, J. Satsuma and T. Tamizhmani, J. Phys. A 51 (2018) 395203. doi: 10.1088/1751-8121/aad8c3
  • R. Willox, A. Ramani and B. Grammaticos, J. Math. Phys. 58 (2017) 123504. doi: 10.1063/1.5004764
  • A. Ramani, B. Grammaticos and T. Tamizhmani, J. Math. Phys. 59 (2018) 113506. doi: 10.1063/1.5042739
  • B. Grammaticos, A. Ramani, K.M. Tamizhmani, T. Tamizhmani and J. Satsuma, J. Math. Phys. 57 (2016) 043506. doi: 10.1063/1.4947061
  • A. Ramani and B. Grammaticos, J. Phys. A 50 (2017) 055204. doi: 10.1088/1751-8121/aa516f
  • A. Ramani, R. Willox, B. Grammaticos, A.S. Carstea and J. Satsuma, Physica A 347 (2005) 1. doi: 10.1016/j.physa.2004.08.086
  • A. Ramani, B. Grammaticos and J. Hietarinta, Phys. Rev. Lett. 67 (1991) 1829. doi: 10.1103/PhysRevLett.67.1829
  • M. Jimbo and H. Sakai, Lett. Math. Phys. 38 (1996) 145. doi: 10.1007/BF00398316
  • M. Jimbo, H. Sakai, A. Ramani and B. Grammaticos, Phys. Lett. A 217 (1996) 111. doi: 10.1016/0375-9601(96)00336-2
  • A. Ramani and B. Grammaticos, Chaos Sol. Frac. 24 (2005) 1331. doi: 10.1016/j.chaos.2004.09.118
  • A. Ramani, Y. Ohta and B. Grammaticos, J. Phys. A 39 (2006) 12167. doi: 10.1088/0305-4470/39/39/S10
  • A. Ramani, Y. Ohta, J. Satsuma and B. Grammaticos, Comm. Math. Phys. 192 (1998) 67. doi: 10.1007/s002200050291
  • A. Fokas, B. Grammaticos and A. Ramani, J. of Math. Anal. and Appl. 180 (1993) 342 doi: 10.1006/jmaa.1993.1405
  • Y. Ohyama and S. Okumura, J. Phys. A 39 (2006) 12129. doi: 10.1088/0305-4470/39/39/S08
  • E.L. Ince, Ordinary Differential Equations, Dover, London, (1956).
  • A. Ramani and B. Grammaticos, Jour. Phys. A 25 (1992) L633. doi: 10.1088/0305-4470/25/11/002
  • A. Ramani and B. Grammaticos, Physica A 228 (1996) 160. doi: 10.1016/0378-4371(95)00439-4

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.