Loading [MathJax]/jax/output/CommonHTML/jax.js
Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






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


Russian Mathematical Surveys, 2011, Volume 66, Issue 1, Pages 107–144
DOI: https://doi.org/10.1070/RM2011v066n01ABEH004729
(Mi rm9403)
 

This article is cited in 9 scientific papers (total in 9 papers)

Singular spectral curves in finite-gap integration

I. A. Taimanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: A number of examples of applications of the method of finite-gap integration of non-linear equations are considered in which singular spectral curves occur. In particular, constructions of orthogonal curvilinear coordinate systems for which a reducible spectral curve consists of rational components are discussed, along with constructions of finite-gap Frobenius manifolds, and a soliton deformation of spectral curves is demonstrated which consists in the creation and annihilation of singular points and corresponds to equations with self-consistent sources.
Bibliography: 52 titles.
Keywords: finite-gap integration, non-linear equations, Riemann surfaces, singular algebraic curves.
Received: 01.12.2010
Bibliographic databases:
Document Type: Article
UDC: 517.957+517.22+514.83
MSC: Primary 37K20, 37K25; Secondary 35Q53
Language: English
Original paper language: Russian
Citation: I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144
Citation in format AMSBIB
\Bibitem{Tai11}
\by I.~A.~Taimanov
\paper Singular spectral curves in finite-gap integration
\jour Russian Math. Surveys
\yr 2011
\vol 66
\issue 1
\pages 107--144
\mathnet{http://mi.mathnet.ru/eng/rm9403}
\crossref{https://doi.org/10.1070/RM2011v066n01ABEH004729}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2841687}
\zmath{https://zbmath.org/?q=an:1235.37024}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2011RuMaS..66..107T}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000294605900004}
\elib{https://elibrary.ru/item.asp?id=20423154}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959556732}
Linking options:
  • https://www.mathnet.ru/eng/rm9403
  • https://doi.org/10.1070/RM2011v066n01ABEH004729
  • https://www.mathnet.ru/eng/rm/v66/i1/p111
  • This publication is cited in the following 9 articles:
    1. P. G. Grinevich, “Riemann Surfaces Close to Degenerate Ones in the Theory of Rogue Waves”, Proc. Steklov Inst. Math., 325 (2024), 86–110  mathnet  crossref  crossref  zmath  isi
    2. A. E. Mironov, A. Senninger, I. A. Taimanov, “Orthogonal Curvilinear Coordinate Systems and Torsion-Free Sheaves over Reducible Spectral Curves”, Math. Notes, 114:4 (2023), 573–582  mathnet  crossref  crossref
    3. P. G. Grinevich, P. M. Santini, “The finite-gap method and the periodic Cauchy problem for (2+1)-dimensional anomalous waves for the focusing Davey–Stewartson 2 equation”, Russian Math. Surveys, 77:6 (2022), 1029–1059  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. Simonetta Abenda, Petr G. Grinevich, “Real regular KP divisors on 𝙼-curves and totally non-negative Grassmannians”, Lett. Math. Phys., 112 (2022), 115–64  mathnet  crossref  scopus
    5. Abenda S. Grinevich P.G., “Reducible M-Curves For Le-Networks in the Totally-Nonnegative Grassmannian and Kp-II Multiline Solitons”, Sel. Math.-New Ser., 25:3 (2019), UNSP 43  crossref  mathscinet  isi
    6. Burban I. Zheglov A., “Fourier-Mukai Transform on Weierstrass Cubics and Commuting Differential Operators”, Int. J. Math., 29:10 (2018), 1850064  crossref  mathscinet  zmath  isi  scopus
    7. Simonetta Abenda, Petr G. Grinevich, “Real soliton lattices of the Kadomtsev–Petviashvili II equation and desingularization of spectral curves: the GrTP(2,4) case”, Proc. Steklov Inst. Math., 302 (2018), 1–15  mathnet  crossref  crossref  mathscinet  isi  elib
    8. O. A. Bogoyavlenskaya, “Ob odnom klasse konechnozonnykh krivolineinykh ortogonalnykh koordinat”, Sib. elektron. matem. izv., 12 (2015), 947–954  mathnet  crossref
    9. E. I. Shamaev, “O reshetkakh Darbu–Egorova v Rn”, Sib. elektron. matem. izv., 10 (2013), 113–122  mathnet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:1352
    Russian version PDF:400
    English version PDF:46
    References:123
    First page:51
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025