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
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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.
@article{ZNSL_1979_84_a10,
author = {I. M. Krichever},
title = {On the rational solutions of {Zakharov--Shabat} equations and completely integrable systems of $N$~particles on a~line},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {117--130},
publisher = {mathdoc},
volume = {84},
year = {1979},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a10/ %G ru %F ZNSL_1979_84_a10
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/