RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
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



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






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


Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 3, Pages 511–529 (Mi izv1364)  

This article is cited in 16 scientific papers (total in 16 papers)

Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves

M. V. Babich, A. I. Bobenko, V. B. Matveev


Abstract: A new approach is given for extracting from general formulas of finite-zone integration solutions of genus $g\geqslant2$ expressible in terms of one-dimensional theta functions. As an application general formulas fo the type of the Lamb Ansatz for genus $g=3$ are found for the sine-Gordon, nonlinear Schrödinger and Koretweg–de Vries equations, and the period matrices of some hyperelliptic curves are computed explicitly.
Bibliography: 35 titles.

Full text: PDF file (1783 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1986, 26:3, 479–496

Bibliographic databases:

UDC: 517.43+519.46
MSC: Primary 35Q20; Secondary 35J10, 35R30, 14K25
Received: 29.06.1983

Citation: M. V. Babich, A. I. Bobenko, V. B. Matveev, “Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves”, Izv. Akad. Nauk SSSR Ser. Mat., 49:3 (1985), 511–529; Math. USSR-Izv., 26:3 (1986), 479–496

Citation in format AMSBIB
\Bibitem{BabBobMat85}
\by M.~V.~Babich, A.~I.~Bobenko, V.~B.~Matveev
\paper Solutions of nonlinear equations integrable in Jacobi theta functions by the method of the inverse problem, and symmetries of algebraic curves
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 3
\pages 511--529
\mathnet{http://mi.mathnet.ru/izv1364}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=794954}
\zmath{https://zbmath.org/?q=an:0657.35021|0583.35012}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 3
\pages 479--496
\crossref{https://doi.org/10.1070/IM1986v026n03ABEH001156}


Linking options:
  • http://mi.mathnet.ru/eng/izv1364
  • http://mi.mathnet.ru/eng/izv/v49/i3/p511

    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. O. Smirnov, “Real finite-gap regular solutions of the Kaup–Boussinesq equation”, Theoret. and Math. Phys., 66:1 (1986), 19–31  mathnet  crossref  mathscinet  zmath  isi
    2. N. N. Akhmediev, V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 69:2 (1986), 1089–1093  mathnet  crossref  mathscinet  zmath  isi
    3. E. D. Belokolos, A. I. Bobenko, V. B. Matveev, V. Z. Ènol'skii, “Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations”, Russian Math. Surveys, 41:2 (1986), 1–49  mathnet  crossref  mathscinet  zmath  isi
    4. N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, “Exact first-order solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 72:2 (1987), 809–818  mathnet  crossref  mathscinet  zmath  isi
    5. A. O. Smirnov, “Finite-gap solutions of Abelian Toda chain of genus 4 and 5 in elliptic functions”, Theoret. and Math. Phys., 78:1 (1989), 6–13  mathnet  crossref  mathscinet  isi
    6. I. A. Taimanov, “Elliptic solutions of nonlinear equations”, Theoret. and Math. Phys., 84:1 (1990), 700–706  mathnet  crossref  mathscinet  zmath  isi
    7. G. L. Alfimov, A. R. Its, N. E. Kulagin, “Modulation instability of solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 84:2 (1990), 787–793  mathnet  crossref  mathscinet  zmath  isi
    8. Min Ho Lee, “The reduction of solutions of some integrable partial differential equations”, Computers & Mathematics with Applications, 25:8 (1993), 95  crossref
    9. A. O. Smirnov, “Elliptic solutions of the nonlinear Schrödinger equation and the modified Korteweg–de Vries equation”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 461–470  mathnet  crossref  mathscinet  zmath  isi
    10. Fritz Gesztesy, Rudi Weikard, “Picard potentials and Hill's equation on a torus”, Acta Math, 176:1 (1996), 73  crossref  mathscinet  zmath  isi
    11. A. O. Smirnov, “Elliptic in $t$ solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 107:2 (1996), 568–578  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. A. O. Smirnov, “On a class of elliptic potentials of the Dirac operator”, Sb. Math., 188:1 (1997), 115–135  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. Fritz Gesztesy, Rudi Weikard, “A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy”, Acta Math, 181:1 (1998), 63  crossref  mathscinet  zmath  isi
    14. A. Treibich, “Hyperelliptic tangential covers and finite-gap potentials”, Russian Math. Surveys, 56:6 (2001), 1107–1151  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. Francisco Correa, Gerald V. Dunne, Mikhail S. Plyushchay, “The Bogoliubov–de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry”, Annals of Physics, 324:12 (2009), 2522  crossref  elib
    16. P. G. Grinevich, P. M. Santini, “Konechnozonnyi podkhod v periodicheskoi zadache Koshi dlya anomalnykh voln v nelineinom uravnenii Shredingera pri nalichii neskolkikh neustoichivykh mod”, UMN, 74:2(446) (2019), 27–80  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:577
    Full text:161
    References:39
    First page:2

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