On the explicit solutions of the elliptic Calogero system

Abstract

Let $q_1,q_2,...,q_N$ be the coordinates of $N$ particles on the circle, interacting with the integrable potential ${\sum }_{j<k}^N\wp (q_j-q_k)$, where $\wp$ is the Weierstrass elliptic function. We show that every symmetric elliptic function in $q_1,q_2,...,q_N$ is a meromorphic function in time. We give explicit formulae for these functions in terms of genus $N-1$ theta functions.

18 pages, Latex

Cited by in corpus (6)

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• Elliptic Solitons and Groebner Bases
• Wannier functions for quasi-periodic finite-gap potentials
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus