RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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


SIGMA, 2010, Volume 6, 044, 29 pages (Mi sigma501)  

This article is cited in 7 scientific papers (total in 7 papers)

Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory

V. S. Gerdjikova, G. G. Grahovskiab

a Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussee, 1784 Sofia, Bulgaria
b School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland

Abstract: The algebraic structure and the spectral properties of a special class of multi-component NLS equations, related to the symmetric spaces of $\mathbf{BD.I}$-type are analyzed. The focus of the study is on the spectral theory of the relevant Lax operators for different fundamental representations of the underlying simple Lie algebra $\mathfrak g$. Special attention is paid to the structure of the dressing factors in spinor representation of the orthogonal simple Lie algebras of $\mathbf B_r\simeq so(2r+1,\mathbb C)$ type.

Keywords: multi-component MNLS equations, reduction group, Riemann–Hilbert problem, spectral decompositions, representation theory

DOI: https://doi.org/10.3842/SIGMA.2010.044

Full text: PDF file (429 kB)
Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/044/
References: PDF file   HTML file

Bibliographic databases:

ArXiv: 1001.1145
Document Type: Article
MSC: 37K20; 35Q51; 74J30; 78A60
Received: January 20, 2010; in final form May 24, 2010; Published online June 2, 2010
Language: English

Citation: V. S. Gerdjikov, G. G. Grahovski, “Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory”, SIGMA, 6 (2010), 044, 29 pp.

Citation in format AMSBIB
\Bibitem{GerGra10}
\by V.~S.~Gerdjikov, G.~G.~Grahovski
\paper Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory
\jour SIGMA
\yr 2010
\vol 6
\papernumber 044
\totalpages 29
\mathnet{http://mi.mathnet.ru/sigma501}
\crossref{https://doi.org/10.3842/SIGMA.2010.044}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2725039}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000278475600009}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84896059201}


Linking options:
  • http://mi.mathnet.ru/eng/sigma501
  • http://mi.mathnet.ru/eng/sigma/v6/p44

    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. Aristophanes Dimakis, Folkert Müller-Hoissen, “Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions”, SIGMA, 6 (2010), 055, 27 pp.  mathnet  crossref  mathscinet
    2. Ma H., Wu D., “Twisted hierarchies associated with the generalized sine-Gordon equation”, J Math Phys, 52:9 (2011), 093704  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Gerdjikov V.S., “On Nonlocal Models of Kulish-Sklyanin Type and Generalized Fourier Transforms”, Advanced Computing in Industrial Mathematics, Studies in Computational Intelligence, 681, eds. Georgiev K., Todorov M., Georgiev I., Springer International Publishing Ag, 2017, 37–52  crossref  mathscinet  isi  scopus
    4. Gerdjikov V.S., Grahovski G.G., Ivanov R.I., “On Integrable Wave Interactions and Lax pairs on Symmetric Spaces”, Wave Motion, 71:SI (2017), 53–70  crossref  mathscinet  isi  scopus
    5. Arnaudon A., Holm D.D., Ivanov R.I., “G-Strands on Symmetric Spaces”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 473:2199 (2017), 20160795  crossref  mathscinet  isi  scopus
    6. G. G. Grahovski, A. Mohammed, H. Susanto, “Nonlocal reductions of the Ablowitz–Ladik equation”, Theoret. and Math. Phys., 197:1 (2018), 1412–1429  mathnet  crossref  crossref  adsnasa  isi  elib
    7. G. G. Grahovski, A. J. Mustafa, H. Susanto, “Nonlocal reductions of the multicomponent nonlinear Schrödinger equation on symmetric spaces”, Theoret. and Math. Phys., 197:1 (2018), 1430–1450  mathnet  crossref  crossref  adsnasa  isi  elib
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:135
    Full text:29
    References:21

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019