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Volume 23, Issue 4, September 2016, Pages 620 - 642
Discretization of Liouville type nonautonomous equations preserving integrals
Authors
Ismagil Habibullin
Institute of Mathematics, Ufa Scientific Center, Russian Academy of Sciences, Chernyshevskii Str., 112. 450077, Ufa, Russia
Bashkir State University, Z.Validi str. 32, Ufa, 450076, Russia,habibullinismagil@gmail.com
Natalya Zheltukhina
Department of Mathematics, Faculty of Science, Bilkent University, 06800, Ankara, Turkey,natalya@fen.bilkent.edu.tr
Received 19 July 2016, Accepted 25 September 2016, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2016.1248159How to use a DOI?
- Keywords
- Semi-discrete chain; Darboux integrability; x-integral; n-integral; continuum limit; discretization
- Abstract
The problem of constructing semi-discrete integrable analogues of the Liouville type integrable PDE is discussed. We call the semi-discrete equation a discretization of the Liouville type PDE if these two equations have a common integral. For the Liouville type integrable equations from the well-known Goursat list for which the integrals of minimal order are of the order less than or equal to two we presented a list of corresponding semi-discrete versions. The list contains new examples of non-autonomous Darboux integrable chains.
- Copyright
- © 2016 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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Cite this article
TY - JOUR AU - Ismagil Habibullin AU - Natalya Zheltukhina PY - 2021 DA - 2021/01/06 TI - Discretization of Liouville type nonautonomous equations preserving integrals JO - Journal of Nonlinear Mathematical Physics SP - 620 EP - 642 VL - 23 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2016.1248159 DO - 10.1080/14029251.2016.1248159 ID - Habibullin2021 ER -