Journal of Nonlinear Mathematical Physics

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
https://doi.org/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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
23 - 4
Pages
620 - 642
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2016.1248159How to use a DOI?
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/).

Cite this article

TY  - JOUR
AU  - Ismagil Habibullin
AU  - Natalya Zheltukhina
PY  - 2021
DA  - 2021/01
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  - https://doi.org/10.1080/14029251.2016.1248159
ID  - Habibullin2021
ER  -