RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 3, Pages 23–44 (Mi izv2784)  

This article is cited in 2 scientific papers (total in 2 papers)

Meromorphic extension of solutions of soliton equations

A. V. Domrin

M. V. Lomonosov Moscow State University

Abstract: We consider local versions of the direct and inverse scattering transforms and describe their analytic properties, which are analogous to the properties of the classical Laplace and Borel transforms. This enables us to study local holomorphic solutions of those integrable equations on $\mathbb C^2_{xt}$ whose complexified forms are given by the zero curvature condition for connections of the form $U dx+V dt$, where $U$ is a linear function of the spectral parameter $z$ and $V$ is a polynomial of degree $m\ge2$ in $z$. We show that the local holomorphic Cauchy problem for such equations is soluble if and only if the scattering data of the initial condition belong to Gevrey class $1/m$. We also show that every local holomorphic solution extends to a global meromorphic function of $x$ for every fixed $t$.

Keywords: soliton equations, analytic continuation.

DOI: https://doi.org/10.4213/im2784

Full text: PDF file (637 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2010, 74:3, 461–480

Bibliographic databases:

Document Type: Article
UDC: 517.958+517.547.24
MSC: 35A07, 37K15
Received: 31.03.2008

Citation: A. V. Domrin, “Meromorphic extension of solutions of soliton equations”, Izv. RAN. Ser. Mat., 74:3 (2010), 23–44; Izv. Math., 74:3 (2010), 461–480

Citation in format AMSBIB
\Bibitem{Dom10}
\by A.~V.~Domrin
\paper Meromorphic extension of solutions of soliton equations
\jour Izv. RAN. Ser. Mat.
\yr 2010
\vol 74
\issue 3
\pages 23--44
\mathnet{http://mi.mathnet.ru/izv2784}
\crossref{https://doi.org/10.4213/im2784}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2682370}
\zmath{https://zbmath.org/?q=an:1202.35186}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2010IzMat..74..461D}
\elib{http://elibrary.ru/item.asp?id=20425207}
\transl
\jour Izv. Math.
\yr 2010
\vol 74
\issue 3
\pages 461--480
\crossref{https://doi.org/10.1070/IM2010v074n03ABEH002494}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000280306100002}
\elib{http://elibrary.ru/item.asp?id=16980374}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78049343971}


Linking options:
  • http://mi.mathnet.ru/eng/izv2784
  • https://doi.org/10.4213/im2784
  • http://mi.mathnet.ru/eng/izv/v74/i3/p23

    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. A. V. Domrin, “On holomorphic solutions of equations of Korteweg–de Vries type”, Trans. Moscow Math. Soc., 73 (2012), 193–206  mathnet  crossref  mathscinet  zmath  elib
    2. A. V. Domrin, “Real-analytic solutions of the nonlinear Schrödinger equation”, Trans. Moscow Math. Soc., 75 (2014), 173–183  mathnet  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:399
    Full text:55
    References:45
    First page:19

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018