Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
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

Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 174, Number 1, Pages 154–176
DOI: https://doi.org/10.4213/tmf8362 (Mi tmf8362) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective

G. F. Helmincka, A. G. Helminckb, E. A. Panasenkoc

a Korteweg-de~Vries Institute, University of Amsterdam, Amsterdam, The Netherlands
b North Carolina State University, Raleigh, USA
c Derzhavin Tambov State University, Tambov, Russia
Full-text PDF (475 kB) Citations (17)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf8362
Abstract: We split the algebra of pseudodifferential operators in two different ways into the direct sum of two Lie subalgebras and deform the set of commuting elements in one subalgebra in the direction of the other component. The evolution of these deformed elements leads to two compatible systems of Lax equations that both have a minimal realization. We show that this Lax form is equivalent to a set of zero-curvature relations. We conclude by presenting linearizations of these systems, which form the key framework for constructing the solutions.
Keywords: integrable deformation, pseudodifferential operator, Lax equation, Kadomtsev–Petviashvili hierarchy, zero-curvature relation, linearization.
Received: 14.05.2012
English version:
Theoretical and Mathematical Physics, 2013, Volume 174, Issue 1, Pages 134–153
DOI: https://doi.org/10.1007/s11232-013-0011-7
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. F. Helminck, A. G. Helminck, E. A. Panasenko, “Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective”, TMF, 174:1 (2013), 154–176; Theoret. and Math. Phys., 174:1 (2013), 134–153
Citation in format AMSBIB
\Bibitem{HelHelPan13}
\by G.~F.~Helminck, A.~G.~Helminck, E.~A.~Panasenko
\paper Integrable deformations in the~algebra of pseudodifferential
operators from a~Lie algebraic perspective
\jour TMF
\yr 2013
\vol 174
\issue 1
\pages 154--176
\mathnet{http://mi.mathnet.ru/tmf8362}
\crossref{https://doi.org/10.4213/tmf8362}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3172958}
\zmath{https://zbmath.org/?q=an:06250986}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2013TMP...174..134H}
\elib{https://elibrary.ru/item.asp?id=20732571}
\transl
\jour Theoret. and Math. Phys.
\yr 2013
\vol 174
\issue 1
\pages 134--153
\crossref{https://doi.org/10.1007/s11232-013-0011-7}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000314532100001}
\elib{https://elibrary.ru/item.asp?id=20433071}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84873586362}
Linking options:
  • https://www.mathnet.ru/eng/tmf8362
  • https://doi.org/10.4213/tmf8362
  • https://www.mathnet.ru/eng/tmf/v174/i1/p154
    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
    Statistics & downloads:
    Abstract page:519
    Full-text PDF :199
    References:74
    First page:13
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024