JMP Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Journal of Mathematical Physics / Volume 53 / Issue 2 / ARTICLES / Methods of Mathematical Physics

J. Math. Phys. 53, 023506 (2012); http://dx.doi.org/10.1063/1.3682240 (24 pages)

Discretising the Painlevé equations à la Hirota-Mickens

B. Grammaticos1, A. Ramani2, J. Satsuma3, and R. Willox4

1IMNC, Université Paris VII & XI, CNRS, UMR 8165, Bât. 440, 91406 Orsay, France
2Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France
3Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara-shi 252-5258, Japan
4Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8914 Tokyo, Japan

View MapView Map

(Received 1 December 2011; accepted 27 December 2011; published online 9 February 2012)

We present a systematic method for discretising the Painlevé equations inspired by the method of Hirota (while extending it) and by that of Mickens (by specifying it to the case at hand). We derive various discrete analogues of Painlevé I and II. We obtain forms that have been previously derived as well as new ones, in particular, equations with a geometry described by the affine Weyl group E8(1). As a by-product we obtain also linearisable equations, some of which are new.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. OUR DISCRETISATION METHOD
  3. DISCRETISING THE PAINLEVÉ I EQUATION
  4. DISCRETISING THE PAINLEVÉ II EQUATION
  5. THE DISCRETISATION OF PAINLEVÉ II REVISITED
  6. CONCLUSIONS AND OUTLOOK

RELATED DATABASES

To view database links for this article, you need to log in.

KEYWORDS and PACS

Keywords

nonlinear differential equations

PACS

  • 02.30.Hq

    Ordinary differential equations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3682240

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    A. Ramani, B. Grammaticos, and J. Hietarinta, Phys. Rev. Lett. 67, 1829 (1991).

    B. Grammaticos, A. Ramani, and V. Papageorgiou, Phys. Rev. Lett. 67, 1825 (1991).

    J. Hietarinta and C. M. Viallet, Phys. Rev. Lett. 81, 325 (1998).


For access to citing articles, you need to log in.



Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. Discretising the Painlevé equations à la Hirota-Mickens
  2. A note on the first integrals of the ABC system
  3. Rational solutions of the Noumi and Yamada system of type A4(1)
  4. Planar waveguide with “twisted” boundary conditions: Small width
  5. Quasi-periodic functions on the torus and sl(n)-elliptic Lie algebra
Go to AIP Home
Copyright © American Institute of Physics
close