Journal of Nonlinear Mathematical Physics

Volume 21, Issue 4, October 2014, Pages 643 - 671

Symmetry reductions and exact solutions of Lax integrable 3-dimensional systems

Authors
H. Baran
Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava, Czech Republic. Hynek.Baran@math.slu.cz
I.S. Krasil'shchik*
Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 746 01 Opava, Czech Republic. 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
*

Permanent address: Independent University of Moscow, B. Vlasevsky 11, 119002 Moscow, Russia

Received 2 July 2014, Accepted 3 September 2014, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2014.975532How to use a DOI?
Keywords
Partial differential equations, symmetry reductions, solutions
Abstract

We present a complete description of 2-dimensional equations that arise as symmetry reductions of four 3- dimensional Lax-integrable equations: (1) the universal hierarchy equation uyy = uzuxy− uyuxz; (2) the 3D rdDym equation uty = uxuxy− uyuxx; (3) the equation uty = utuxy− uyutx, which we call modified Veronese web equation; (4) Pavlov's equation uyy = utx + uyuxx− uxuxy.

Copyright
© 2014 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/).

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
21 - 4
Pages
643 - 671
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2014.975532How to use a DOI?
Copyright
© 2014 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  - H. Baran
AU  - I.S. Krasil'shchik
AU  - O.I. Morozov
AU  - P. Vojčák
PY  - 2021
DA  - 2021/01
TI  - Symmetry reductions and exact solutions of Lax integrable 3-dimensional systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 643
EP  - 671
VL  - 21
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2014.975532
DO  - https://doi.org/10.1080/14029251.2014.975532
ID  - Baran2021
ER  -