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

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Teoreticheskaya i Matematicheskaya Fizika, 1999, Volume 121, Number 3, Pages 367–373
DOI: https://doi.org/10.4213/tmf816 (Mi tmf816)

This article is cited in 11 scientific papers (total in 11 papers)

Algebraic-geometric solutions of the Krichever–Novikov equation

D. P. Novikov

Omsk State Technical University

Full-text PDF (206 kB) Citations (11)

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

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.

Received: 11.12.1998
Revised: 22.04.1999

English version:
Theoretical and Mathematical Physics, 1999, Volume 121, Issue 3, Pages 1567–1573
DOI: https://doi.org/10.1007/BF02557203

Bibliographic databases:

Language: Russian

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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\vol 121

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\pages 1567--1573

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Linking options:

https://www.mathnet.ru/eng/tmf816

https://doi.org/10.4213/tmf816

https://www.mathnet.ru/eng/tmf/v121/i3/p367

This publication is cited in the following 11 articles:

Wei Fu, Shi-Hao Li, “Skew-Orthogonal Polynomials and Pfaff Lattice Hierarchy Associated With an Elliptic Curve”, International Mathematics Research Notices, 2024
Petlenko A.V., “Analysis of the Polarization of the Electric-Field Component of High-Latitude Pulsations of the Pc1 Range in the Coastal Zone”, Geomagn. Aeron., 61:2 (2021), 191–200
Igonin S., Manno G., “On Lie Algebras Responsible For Integrability of (1+1)-Dimensional Scalar Evolution Pdes”, J. Geom. Phys., 150 (2020), 103596
Igonin S., Manno G., “Lie Algebras Responsible For Zero-Curvature Representations of Scalar Evolution Equations”, J. Geom. Phys., 138 (2019), 297–316
Wang J. Xiong N. Li B., “Peakon Solutions of Alice-Bob B-Family Equation and Novikov Equation”, Adv. Math. Phys., 2019, 1519305
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
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
Decio Levi, Pavel Winternitz, Ravil I. Yamilov, “Symmetries of the Continuous and Discrete Krichever–Novikov Equation”, SIGMA, 7 (2011), 097, 16 pp.
Pavel Winternitz, Symmetries and Integrability of Difference Equations, 2011, 292
Levi D., Winternitz P., Yamilov R.I., “Lie point symmetries of differential-difference equations”, J. Phys. A: Math. Theor., 43:29 (2010), 292002
Igonin, S, “Prolongation structure of the Krichever-Novikov equation”, Journal of Physics A-Mathematical and General, 35:46 (2002), 9801

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	673
Full-text PDF :	279
References:	89
First page:	2

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