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TMF, 1989, Volume 78, Number 1, Pages 11–21 (Mi tmf4712)  

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

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

A. O. Smirnov


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.

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English version:
Theoretical and Mathematical Physics, 1989, 78:1, 6–13

Bibliographic databases:

Received: 09.06.1987

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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\by A.~O.~Smirnov
\paper Finite-gap solutions of~Abelian Toda chain of~genus~4 and 5 in~elliptic functions
\jour TMF
\yr 1989
\vol 78
\issue 1
\pages 11--21
\mathnet{http://mi.mathnet.ru/tmf4712}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=987408}
\transl
\jour Theoret. and Math. Phys.
\yr 1989
\vol 78
\issue 1
\pages 6--13
\crossref{https://doi.org/10.1007/BF01016911}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1989AL44300002}


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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. A. O. Smirnov, “Real elliptic solutions of the “sine-Gordon” equation”, Math. USSR-Sb., 70:1 (1991), 231–240  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. A. Taimanov, “Elliptic solutions of nonlinear equations”, Theoret. and Math. Phys., 84:1 (1990), 700–706  mathnet  crossref  mathscinet  zmath  isi
    3. 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
    4. A. O. Smirnov, “Solutions of the KdV equation elliptic in $t$”, Theoret. and Math. Phys., 100:2 (1994), 937–947  mathnet  crossref  mathscinet  zmath  isi
    5. A. O. Smirnov, “Two-gap elliptic solutions to integrable nonlinear equations”, Math. Notes, 58:1 (1995), 735–743  mathnet  crossref  mathscinet  zmath  isi
    6. 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
    7. 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  mathnet  elib
    8. A. O. Smirnov, “Elliptic breather for nonlinear Shrödinger equation”, J. Math. Sci. (N. Y.), 192:1 (2013), 117–125  mathnet  crossref  mathscinet
    9. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    10. A. O. Smirnov, G. M. Golovachev, “Trekhfaznye resheniya nelineinogo uravneniya Shredingera v ellipticheskikh funktsiyakh”, Nelineinaya dinam., 9:3 (2013), 389–407  mathnet
    11. 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  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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