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Rational solutions of the Zakharov-Shabat equations and completely integrable systems of N particles on a line

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Abstract

One constructs all the decreasing rational solutions of the Kadomtsev-Petviashvili equations. The presented method allows us to identify the motion of the poles of the obtained functions with the motion of a system of N particles on a line with a Hamiltonian of the Calogero-Moser type. Thus, this Hamiltonian system is imbedded in the theory of the algebraic-geometric solutions of the Zakharov-Shabat equations.

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Literature cited

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Authors
  1. I. M. Krichever
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 84, pp. 117–130, 1979.

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Krichever, I.M. Rational solutions of the Zakharov-Shabat equations and completely integrable systems of N particles on a line. J Math Sci 21, 335–345 (1983). https://doi.org/10.1007/BF01660590

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