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TMF, 1999, Volume 121, Number 3, Pages 367–373 (Mi tmf816)  

This article is cited in 6 scientific papers (total in 6 papers)

Algebraic-geometric solutions of the Krichever–Novikov equation

D. P. Novikov

Omsk State Technical University

Abstract: A zero-curvature representation with constant poles on an elliptic curve is obtained for the Krichever–Novikov equation. Algebraic-geometric solutions of this equation are constructed. The consideration is based on reducing the theta function of a two-sheet covering of an elliptic curve to the Prym theta functions of codimension one.

DOI: https://doi.org/10.4213/tmf816

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English version:
Theoretical and Mathematical Physics, 1999, 121:3, 1567–1573

Bibliographic databases:

Received: 11.12.1998
Revised: 22.04.1999

Citation: D. P. Novikov, “Algebraic-geometric solutions of the Krichever–Novikov equation”, TMF, 121:3 (1999), 367–373; Theoret. and Math. Phys., 121:3 (1999), 1567–1573

Citation in format AMSBIB
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\paper Algebraic-geometric solutions of the Krichever--Novikov equation
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\pages 367--373
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 121
\issue 3
\pages 1567--1573
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    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. Igonin, S, “Prolongation structure of the Krichever-Novikov equation”, Journal of Physics A-Mathematical and General, 35:46 (2002), 9801  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Levi D., Winternitz P., Yamilov R.I., “Lie point symmetries of differential-difference equations”, J. Phys. A: Math. Theor., 43:29 (2010), 292002  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    3. Decio Levi, Pavel Winternitz, Ravil I. Yamilov, “Symmetries of the Continuous and Discrete Krichever–Novikov Equation”, SIGMA, 7 (2011), 097, 16 pp.  mathnet  crossref  mathscinet
    4. V. N. Davletshina, “Self-Adjoint Commuting Differential Operators of Rank 2 and Their Deformations Given by Soliton Equations”, Math. Notes, 97:3 (2015), 333–340  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Kou K. Li J., “Exact Traveling Wave Solutions of the Krichever-Novikov Equation: a Dynamical System Approach”, Int. J. Bifurcation Chaos, 27:4 (2017), 1750058  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Igonin S., Manno G., “Lie Algebras Responsible For Zero-Curvature Representations of Scalar Evolution Equations”, J. Geom. Phys., 138 (2019), 297–316  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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