Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




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

Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 070, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.070 (Mi sigma98) 		 
This article is cited in 21 scientific papers (total in 21 papers)

On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa–Holm Equation

Henrik Aratyna, Jose Francisco Gomesb, Abraham H. Zimermanb

a Department of Physics, University of Illinois at Chicago, 845 W. Taylor St., Chicago, Illinois 60607-7059
b Instituto de Física Teórica-UNESP, Rua Pamplona 145, 01405-900 São Paulo, Brazil
Full-text PDF (223 kB) Citations (21)
References:
PDF
HTML
DOI: https://doi.org/10.3842/SIGMA.2006.070
Abstract: Different gauge copies of the Ablowitz–Kaup–Newell–Segur (AKNS) model labeled by an angle $\theta$ are constructed and then reduced to the two-component Camassa–Holm model. Only three different independent classes of reductions are encountered corresponding to the angle $\theta$ being 0, $\pi/2$ or taking any value in the interval $0<\theta<\pi/2$. This construction induces Bäcklund transformations between solutions of the two-component Camassa–Holm model associated with different classes of reduction.
Keywords: integrable hierarchies; Camassa–Holm equation; Bäcklund transformation.
Received: September 13, 2006; in final form October 5, 2006; Published online October 17, 2006
Bibliographic databases:
Document Type: Article
MSC: 37K10; 35Q53; 53A07; 53B50
Language: English
Citation: Henrik Aratyn, Jose Francisco Gomes, Abraham H. Zimerman, “On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa–Holm Equation”, SIGMA, 2 (2006), 070, 12 pp.
Citation in format AMSBIB
\Bibitem{AraGomZim06}
\by Henrik Aratyn, Jose Francisco Gomes, Abraham H.~Zimerman
\paper On a~Negative Flow of the AKNS Hierarchy and Its Relation to a~Two-Component Camassa--Holm Equation
\jour SIGMA
\yr 2006
\vol 2
\papernumber 070
\totalpages 12
\mathnet{http://mi.mathnet.ru/sigma98}
\crossref{https://doi.org/10.3842/SIGMA.2006.070}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2264886}
\zmath{https://zbmath.org/?q=an:1131.37059}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000207065100069}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889236969}
Linking options:
  • https://www.mathnet.ru/eng/sigma98
  • https://www.mathnet.ru/eng/sigma/v2/p70
    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:295
    Full-text PDF :64
    References:52
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024