A. O. Smirnov, “Finite-gap solutions of Abelian Toda chain of genus 4 and 5 in elliptic functions”, TMF, 78:1 (1989), 11–21; Theoret. and Math. Phys., 78:1 (1989), 6

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Teoreticheskaya i Matematicheskaya Fizika, 1989, Volume 78, Number 1, Pages 11–21 (Mi tmf4712)

This article is cited in 17 scientific papers (total in 17 papers)

Finite-gap solutions of Abelian Toda chain of genus 4 and 5 in elliptic functions

A. O. Smirnov

Full-text PDF (948 kB) Citations (17)

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Abstract: A reduction theorem is formulated and proved. Smooth real solutions of the abelian Toda lattice of the genus 4 and 5 are obtained in terms of the elliptic functions. In terms of the

$g$ -dimensional theta-functions the solutions of the genus

$2g$ and

$2g+1$ are constructed for the discrete Peierls–Fröhlich model in the absence of intramolecular deformation.

Received: 09.06.1987

English version:
Theoretical and Mathematical Physics, 1989, Volume 78, Issue 1, Pages 6–13
DOI: https://doi.org/10.1007/BF01016911

Bibliographic databases:

Language: Russian

Citation: A. O. Smirnov, “Finite-gap solutions of Abelian Toda chain of genus 4 and 5 in elliptic functions”, TMF, 78:1 (1989), 11–21; Theoret. and Math. Phys., 78:1 (1989), 6–13

Citation in format AMSBIB

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\paper Finite-gap solutions of~Abelian Toda chain of~genus~4 and 5 in~elliptic functions

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\issue 1

\pages 11--21

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\transl

\jour Theoret. and Math. Phys.

\yr 1989

\vol 78

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\pages 6--13

\crossref{https://doi.org/10.1007/BF01016911}

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Linking options:

https://www.mathnet.ru/eng/tmf4712

https://www.mathnet.ru/eng/tmf/v78/i1/p11

This publication is cited in the following 17 articles:

A. O. Smirnov, “Konechnozonnye resheniya uravneniya mKdF: klassicheskaya i alternativnye formuly”, Algebra i analiz, 37:2 (2025), 156–176
I T Habibullin, A R Khakimova, A O Smirnov, “Construction of exact solutions to the Ruijsenaars–Toda lattice via generalized invariant manifolds”, Nonlinearity, 36:1 (2023), 231
V. B. Matveev, A. O. Smirnov, “Dubrovin method and Toda lattice”, St. Petersburg Math. J., 34:6 (2023), 1019–1037
A. Smirnov, M. Pavlov, V. Matveev, V. Gerdjikov, Proceedings of Symposia in Pure Mathematics, 103.1, Integrability, Quantization, and Geometry, 2021, 429
V. B. Matveev, A. O. Smirnov, “Elliptic solitons and «freak waves»”, St. Petersburg Math. J., 33:3 (2022), 523–551
V. B. Matveev, A. O. Smirnov, “Two-phase periodic solutions to the AKNS hierarchy equations”, J. Math. Sci. (N. Y.), 242:5 (2019), 722–741
A. O. Smirnov, G. M. Golovachev, “Trekhfaznye resheniya nelineinogo uravneniya Shredingera v ellipticheskikh funktsiyakh”, Nelineinaya dinam., 9:3 (2013), 389–407
A. O. Smirnov, “Elliptic breather for nonlinear Shrödinger equation”, J. Math. Sci. (N. Y.), 192:1 (2013), 117–125
A. O. Smirnov, “Solution of a nonlinear Schrödinger equation in the form of two-phase freak waves”, Theoret. and Math. Phys., 173:1 (2012), 1403–1416
A. O. Smirnov, G. M. Golovachev, E. G. Amosenok, “Dvukhzonnye 3-ellipticheskie resheniya uravnenii Bussineska i Kortevega–de Friza”, Nelineinaya dinam., 7:2 (2011), 239–256
Evgeniy Gennadievich Amosenok, Aleksandr Olegovich Smirnov, “Two-Gap Two-Elliptic Solution of Boussinesq Equation”, Lett Math Phys, 96:1-3 (2011), 157
A. O. Smirnov, “Elliptic in $t$ solutions of the nonlinear Schrödinger equation”, Theoret. and Math. Phys., 107:2 (1996), 568–578
A. O. Smirnov, “Two-gap elliptic solutions to integrable nonlinear equations”, Math. Notes, 58:1 (1995), 735–743
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
A. O. Smirnov, “Solutions of the KdV equation elliptic in $t$ ”, Theoret. and Math. Phys., 100:2 (1994), 937–947
A. O. Smirnov, “Real elliptic solutions of the “sine-Gordon” equation”, Math. USSR-Sb., 70:1 (1991), 231–240
I. A. Taimanov, “Elliptic solutions of nonlinear equations”, Theoret. and Math. Phys., 84:1 (1990), 700–706

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

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