RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2018, Volume 196, Number 2, Pages 169–192 (Mi tmf9452)  

This article is cited in 2 scientific papers (total in 2 papers)

Nonlocal symmetries of integrable linearly degenerate equations: A comparative study

H. Barana, I. S. Krasil'shchikbc, O. I. Morozovd, P. Vojčáka

a Mathematical Institute, Silesian University in Opava, Opava, Czech Republic
b V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
c Independent University of Moscow, Moscow, Russia
d Faculty of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland

Abstract: We continue the study of Lax integrable equations. We consider four three-dimensional equations{: (1)} the rdDym equation $u_{ty}=u_xu_{xy}- u_yu_{xx}$, $(2)$ the Pavlov equation $u_{yy}=u_{tx}+u_yu_{xx}-u_xu_{xy}$, $(3)$ the universal hierarchy equation $u_{yy}=u_tu_{xy}-u_yu_{tx}$, and $(4)$ the modified Veronese web equation $u_{ty}=u_tu_{xy}-u_yu_{tx}$. For each equation, expanding the known Lax pairs in formal series in the spectral parameter, we construct two differential coverings and completely describe the nonlocal symmetry algebras associated with these coverings. For all four pairs of coverings, the obtained Lie algebras of symmetries manifest similar (but not identical) structures; they are (semi)direct sums of the Witt algebra, the algebra of vector fields on the line, and loop algebras, all of which contain a component of finite grading. We also discuss actions of recursion operators on shadows of nonlocal symmetries.

Keywords: partial differential equation, integrable linearly degenerate equation, nonlocal symmetry, recursion operator.

Funding Agency Grant Number
Dobrushin Foundation
Ministry of Science and Higher Education (Poland)
Netherlands Enterprise Agency IČ47813059
The research of I. S. Krasilshchik was supported in part by a grant “Dobrushin Professorship–2017.” The research of O. I. Morozov was supported by the Polish Ministry of Science and Higher Education. The research of H. Baran and P. Vojčák was supported by RVO funding for IČ47813059.


DOI: https://doi.org/10.4213/tmf9452

Full text: PDF file (674 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2018, 196:2, 1089–1110

Bibliographic databases:

Received: 30.08.2017

Citation: H. Baran, I. S. Krasil'shchik, O. I. Morozov, P. Vojčák, “Nonlocal symmetries of integrable linearly degenerate equations: A comparative study”, TMF, 196:2 (2018), 169–192; Theoret. and Math. Phys., 196:2 (2018), 1089–1110

Citation in format AMSBIB
\Bibitem{BarKraMor18}
\by H.~Baran, I.~S.~Krasil'shchik, O.~I.~Morozov, P.~Voj{\v{c}}\'ak
\paper Nonlocal symmetries of integrable linearly degenerate equations: A~comparative study
\jour TMF
\yr 2018
\vol 196
\issue 2
\pages 169--192
\mathnet{http://mi.mathnet.ru/tmf9452}
\crossref{https://doi.org/10.4213/tmf9452}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...196.1089B}
\elib{http://elibrary.ru/item.asp?id=35276539}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 196
\issue 2
\pages 1089--1110
\crossref{https://doi.org/10.1134/S0040577918080019}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000443722200001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052680485}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9452
  • https://doi.org/10.4213/tmf9452
  • http://mi.mathnet.ru/eng/tmf/v196/i2/p169

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Holba P., Krasil'shchik I.S., Morozov O.I., Vojcak P., “Reductions of the Universal Hierarchy and Rddym Equations and Their Symmetry Properties”, Lobachevskii J. Math., 39:5 (2018), 673–681  crossref  isi
    2. Krasil'shchik I., Sergyeyev A., “Integrability of Anti-Self-Dual Vacuum Einstein Equations With Nonzero Cosmological Constant: An Infinite Hierarchy of Nonlocal Conservation Laws”, Ann. Henri Poincare, 20:8 (2019), 2699–2715  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:129
    References:18
    First page:15

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020