RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






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


Tr. Mat. Inst. Steklova, 2006, Volume 255, Pages 180–196 (Mi tm262)  

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

Orthogonal Curvilinear Coordinate Systems Corresponding to Singular Spectral Curves

A. E. Mironov, I. A. Taimanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We study the limiting case of the Krichever construction of orthogonal curvilinear coordinate systems when the spectral curve becomes singular. We show that when the curve is reducible and all its irreducible components are rational curves, the construction procedure reduces to solving systems of linear equations and to simple computations with elementary functions. We also demonstrate how well-known coordinate systems, such as polar coordinates, cylindrical coordinates, and spherical coordinates in Euclidean spaces, fit in this scheme.

Full text: PDF file (256 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 255, 169–184

Bibliographic databases:

UDC: 517.957
Received in December 2005

Citation: A. E. Mironov, I. A. Taimanov, “Orthogonal Curvilinear Coordinate Systems Corresponding to Singular Spectral Curves”, Function spaces, approximation theory, and nonlinear analysis, Collected papers, Tr. Mat. Inst. Steklova, 255, Nauka, MAIK Nauka/Inteperiodika, M., 2006, 180–196; Proc. Steklov Inst. Math., 255 (2006), 169–184

Citation in format AMSBIB
\Bibitem{MirTai06}
\by A.~E.~Mironov, I.~A.~Taimanov
\paper Orthogonal Curvilinear Coordinate Systems Corresponding to Singular Spectral Curves
\inbook Function spaces, approximation theory, and nonlinear analysis
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2006
\vol 255
\pages 180--196
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm262}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2301618}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 255
\pages 169--184
\crossref{https://doi.org/10.1134/S0081543806040146}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846881542}


Linking options:
  • http://mi.mathnet.ru/eng/tm262
  • http://mi.mathnet.ru/eng/tm/v255/p180

    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. E. Mironov, I. A. Taimanov, “Some algebraic examples of Frobenius manifolds”, Theoret. and Math. Phys., 151:2 (2007), 604–613  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. I. P. Rybnikov, “Minimal Lagrangian submanifolds in $\mathbb C\mathrm P^n$ with diagonal metric”, Siberian Math. J., 52:1 (2011), 105–112  mathnet  crossref  mathscinet  isi
    4. D. A. Berdinskii, I. P. Rybnikov, “On orthogonal curvilinear coordinate systems in constant curvature spaces”, Siberian Math. J., 52:3 (2011), 394–401  mathnet  crossref  mathscinet  isi
    5. E. I. Shamaev, “O reshetkakh Darbu–Egorova v ${\mathbb R}^n$”, Sib. elektron. matem. izv., 10 (2013), 113–122  mathnet
    6. O. A. Bogoyavlenskaya, “Ob odnom klasse konechnozonnykh krivolineinykh ortogonalnykh koordinat”, Sib. elektron. matem. izv., 12 (2015), 947–954  mathnet  crossref
    7. E. I. Shamaev, “O diskretizatsii parabolicheskikh koordinat”, Sib. elektron. matem. izv., 13 (2016), 1159–1169  mathnet  crossref
    8. O. I. Mokhov, “O metrikakh diagonalnoi krivizny”, Fundament. i prikl. matem., 21:6 (2016), 171–182  mathnet
    9. O. I. Mokhov, “Pencils of compatible metrics and integrable systems”, Russian Math. Surveys, 72:5 (2017), 889–937  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  •    . . .  Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:951
    Full text:246
    References:50

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