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, 2008, Volume 156, Number 1, Pages 67–76
DOI: https://doi.org/10.4213/tmf6230 (Mi tmf6230) 		 
System of equations for stimulated combination scattering and the related double periodic $A_n^{(1)}$ Toda chains

V. A. Andreev

P. N. Lebedev Physical Institute, Russian Academy of Sciences
Full-text PDF (393 kB)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf6230
Abstract: We consider a system of equations describing stimulated combination scattering of light. We show that solutions of this system are expressed in terms of two solutions of the sine-Gordon equation that are related to each other by a Bäcklund transformation. We also show that this system is integrable and admits a Zakharov–Shabat pair. In the general case, the system of equations for the Bäcklund transformation of periodic $A_n^{(1)}$ Toda chains is also shown to be integrable and to have a Zakharov–Shabat pair.
Keywords: combination scattering, Toda chain, Bäcklund transformation, Zakharov–Shabat pair.
Received: 29.03.2007
Revised: 22.06.2007
English version:
Theoretical and Mathematical Physics, 2008, Volume 156, Issue 1, Pages 1020–1027
DOI: https://doi.org/10.1007/s11232-008-0095-7
Bibliographic databases:
Language: Russian
Citation: V. A. Andreev, “System of equations for stimulated combination scattering and the related double periodic $A_n^{(1)}$ Toda chains”, TMF, 156:1 (2008), 67–76; Theoret. and Math. Phys., 156:1 (2008), 1020–1027
Citation in format AMSBIB
\Bibitem{And08}
\by V.~A.~Andreev
\paper System of equations for stimulated combination scattering
and the~related double periodic $A_n^{(1)}$ Toda chains
\jour TMF
\yr 2008
\vol 156
\issue 1
\pages 67--76
\mathnet{http://mi.mathnet.ru/tmf6230}
\crossref{https://doi.org/10.4213/tmf6230}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2488212}
\zmath{https://zbmath.org/?q=an:1185.37152}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2008TMP...156.1020A}
\transl
\jour Theoret. and Math. Phys.
\yr 2008
\vol 156
\issue 1
\pages 1020--1027
\crossref{https://doi.org/10.1007/s11232-008-0095-7}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000258719900003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-51649095398}
Linking options:
  • https://www.mathnet.ru/eng/tmf6230
  • https://doi.org/10.4213/tmf6230
  • https://www.mathnet.ru/eng/tmf/v156/i1/p67
    • 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:596
    Full-text PDF :224
    References:85
    First page:6
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024