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 197, Number 1, Pages 68–88 (Mi tmf9577)  

Soliton scattering in noncommutative spaces

M. Hamanaka, H. Okabe

Graduate School of Mathematics, Nagoya University, Nagoya, Japan

Abstract: We discuss exact multisoliton solutions of integrable hierarchies on noncommutative space–times in various dimensions. The solutions are represented by quasideterminants in compact forms. We study soliton scattering processes in the asymptotic region where the configurations can be real-valued. We find that the asymptotic configurations in the soliton scatterings can all be the same as commutative ones, i.e., the configuration of an $N$-soliton solution has $N$ isolated localized lumps of energy, and each solitary wave-packet lump preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. As new results, we present multisoliton solutions of the noncommutative anti-self-dual Yang–Mills hierarchy and discuss two-soliton scattering in detail.

Keywords: soliton, integrable system, noncommutative geometry.

Funding Agency Grant Number
Japan Society for the Promotion of Science 16K05318
The research of M. Hamanaka was supported by a Grant-in-Aid for Scientific Research (No. 16K05318).


DOI: https://doi.org/10.4213/tmf9577

Full text: PDF file (566 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2018, 197:1, 1451–1468

Bibliographic databases:

Received: 05.04.2018

Citation: M. Hamanaka, H. Okabe, “Soliton scattering in noncommutative spaces”, TMF, 197:1 (2018), 68–88; Theoret. and Math. Phys., 197:1 (2018), 1451–1468

Citation in format AMSBIB
\Bibitem{HamOka18}
\by M.~Hamanaka, H.~Okabe
\paper Soliton scattering in noncommutative spaces
\jour TMF
\yr 2018
\vol 197
\issue 1
\pages 68--88
\mathnet{http://mi.mathnet.ru/tmf9577}
\crossref{https://doi.org/10.4213/tmf9577}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018TMP...197.1451H}
\elib{http://elibrary.ru/item.asp?id=35601325}
\transl
\jour Theoret. and Math. Phys.
\yr 2018
\vol 197
\issue 1
\pages 1451--1468
\crossref{https://doi.org/10.1134/S0040577918100045}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000449768100004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85056091339}


Linking options:
  • http://mi.mathnet.ru/eng/tmf9577
  • https://doi.org/10.4213/tmf9577
  • http://mi.mathnet.ru/eng/tmf/v197/i1/p68

    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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:124
    References:20
    First page:9

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