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Zap. Nauchn. Sem. LOMI, 1979, Volume 84, Pages 117–130 (Mi znsl2938)  

This article is cited in 5 scientific papers (total in 5 papers)

On the rational solutions of Zakharov–Shabat equations and completely integrable systems of $N$ particles on a line

I. M. Krichever


Abstract: All decreasing rational solutions of the Kadomtzev–Petviashvili equations are constructed. The motion of the poles of a solution is identified with the motion of $N$ particles on the line via Calogero–Moser hamiltonians. This Hamiltonian system is thus included in the theory of algebro-geometric solutions of Zakharov–Shabat equations.

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English version:
Journal of Soviet Mathematics, 1983, 21:3, 335–345

Bibliographic databases:

UDC: 517.93

Citation: I. M. Krichever, “On the rational solutions of Zakharov–Shabat equations and completely integrable systems of $N$ particles on a line”, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Zap. Nauchn. Sem. LOMI, 84, "Nauka", Leningrad. Otdel., Leningrad, 1979, 117–130; J. Soviet Math., 21:3 (1983), 335–345

Citation in format AMSBIB
\Bibitem{Kri79}
\by I.~M.~Krichever
\paper On the rational solutions of Zakharov--Shabat equations and completely integrable systems of $N$~particles on a~line
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~11
\serial Zap. Nauchn. Sem. LOMI
\yr 1979
\vol 84
\pages 117--130
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2938}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=557031}
\zmath{https://zbmath.org/?q=an:0413.35008|0515.35005}
\transl
\jour J. Soviet Math.
\yr 1983
\vol 21
\issue 3
\pages 335--345
\crossref{https://doi.org/10.1007/BF01660590}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. G. Novikov, G. M. Henkin, “Oscillating weakly localized solutions of the Korteweg–de Vries equation”, Theoret. and Math. Phys., 61:2 (1984), 1089–1099  mathnet  crossref  mathscinet  zmath  isi
    2. V. M. Buchstaber, D. V. Leikin, V. Z. Ènol'skii, “Rational Analogs of Abelian Functions”, Funct. Anal. Appl., 33:2 (1999), 83–94  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. B. Matveev, “Positons: Slowly Decreasing Analogues of Solitons”, Theoret. and Math. Phys., 131:1 (2002), 483–497  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. A. V. Zabrodin, “The master $T$-operator for vertex models with trigonometric $R$-matrices as a classical $\tau$-function”, Theoret. and Math. Phys., 174:1 (2013), 52–67  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Anton Zabrodin, “The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy”, SIGMA, 10 (2014), 006, 18 pp.  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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