Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 117-130
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I. M. Krichever. On the rational solutions of Zakharov–Shabat equations and completely integrable systems of $N$ particles on a line. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 117-130. http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a10/
@article{ZNSL_1979_84_a10,
author = {I. M. Krichever},
title = {On the rational solutions of {Zakharov{\textendash}Shabat} equations and completely integrable systems of $N$~particles on a~line},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {117--130},
year = {1979},
volume = {84},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a10/}
}
TY - JOUR
AU - I. M. Krichever
TI - On the rational solutions of Zakharov–Shabat equations and completely integrable systems of $N$ particles on a line
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1979
SP - 117
EP - 130
VL - 84
UR - http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a10/
LA - ru
ID - ZNSL_1979_84_a10
ER -
%0 Journal Article
%A I. M. Krichever
%T On the rational solutions of Zakharov–Shabat equations and completely integrable systems of $N$ particles on a line
%J Zapiski Nauchnykh Seminarov POMI
%D 1979
%P 117-130
%V 84
%U http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a10/
%G ru
%F ZNSL_1979_84_a10
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.
