Geodesic
Elliptic Families of Solutions of the Kadomtsev--Petviashvili Equation and the Field Elliptic Calogero--Moser System
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 1-17

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We present a Lax pair for the field elliptic Calogero–Moser system and establish a connection between this system and the Kadomtsev–Petviashvili equation. Namely, we consider elliptic families of solutions of the KP equation such that their poles satisfy a constraint of being balanced. We show that the dynamics of these poles is described by a reduction of the field elliptic CM system. We construct a wide class of solutions to the field elliptic CM system by showing that any $N$-fold branched cover of an elliptic curve gives rise to an elliptic family of solutions of the KP equation with balanced poles.
Mots-clés : KP equation, Calogero–Moser system, Lax pair. 
@article{FAA_2002_36_4_a0,
     author = {A. A. Akhmetshin and Yu. S. Vol'vovskii and I. M. Krichever},
     title = {Elliptic {Families} of {Solutions} of the {Kadomtsev--Petviashvili} {Equation} and the {Field} {Elliptic} {Calogero--Moser} {System}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {1--17},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a0/}
}
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A. A. Akhmetshin; Yu. S. Vol'vovskii; I. M. Krichever. Elliptic Families of Solutions of the Kadomtsev--Petviashvili Equation and the Field Elliptic Calogero--Moser System. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 1-17. http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a0/