Journal of Nonlinear Mathematical Physics

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Volume 24, Issue Supplement 1, December 2017, Pages 36 - 47

2D reductions of the equation uyy = utx + uyuxx − uxuxy and their nonlocal symmetries

Authors
P. Holba
Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava, Czech Republic.M160016@math.slu.cz
I.S. Krasil'shchik
Independent University of Moscow, B. Vlasevsky 11, 119002 Moscow, Russia, Russian State University for Humanities, Miusskaya sq. 6, Moscow, GSP-3, 125993, Russia & Trapeznikov Institute of Control Sciences, 65 Profsoyuznaya street, Moscow 117997, Russia,josephkra@gmail.com
O.I. Morozov
Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, Kraków 30-059, Poland.morozov@agh.edu.pl
P. Vojčák
Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava, Czech Republic.Petr.Vojcak@math.slu.cz
Received 24 July 2017, Accepted 29 August 2017, Available Online 6 January 2021.
DOI
10.1080/14029251.2017.1418052How to use a DOI?
Keywords
Partial differential equations; Lax integrable equations; symmetry reductions; nonlocal symmetries; Gibbons-Tsarev equation
Abstract

We consider the 3D equation uyy = utx + uyuxx − uxuxy and its 2D symmetry reductions: (1) uyy = (uy + y) uxx − uxuxy − 2 (which is equivalent to the Gibbons-Tsarev equation) and (2) uyy = (uy + 2x)uxx + (y − ux)uxy − ux. Using the corresponding reductions of the known Lax pair for the 3D equation, we describe nonlocal symmetries of (1) and (2) and show that the Lie algebras of these symmetries are isomorphic to the Witt algebra.

Copyright
© 2017 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
24 - Supplement 1
Pages
36 - 47
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2017.1418052How to use a DOI?
Copyright
© 2017 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

risenwbib
TY  - JOUR
AU  - P. Holba
AU  - I.S. Krasil'shchik
AU  - O.I. Morozov
AU  - P. Vojčák
PY  - 2021
DA  - 2021/01/06
TI  - 2D reductions of the equation uyy = utx + uyuxx − uxuxy and their nonlocal symmetries
JO  - Journal of Nonlinear Mathematical Physics
SP  - 36
EP  - 47
VL  - 24
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2017.1418052
DO  - 10.1080/14029251.2017.1418052
ID  - Holba2021
ER  -