dorsal/arxiv
View SchemaOn the explicit solutions of the elliptic Calogero system
| Authors | L. Gavrilov, A. Perelomov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9905011 |
| URL | https://arxiv.org/abs/solv-int/9905011 |
| DOI | 10.1063/1.533096 |
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.
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"abstract": "Let $q_1,q_2,...,q_N$ be the coordinates of $N$ particles on the circle,\ninteracting with the integrable potential $\\sum_{j\u003ck}^N\\wp(q_j-q_k)$, where\n$\\wp$ is the Weierstrass elliptic function. We show that every symmetric\nelliptic function in $q_1,q_2,...,q_N$ is a meromorphic function in time. We\ngive explicit formulae for these functions in terms of genus $N-1$ theta\nfunctions.",
"arxiv_id": "solv-int/9905011",
"authors": [
"L. Gavrilov",
"A. Perelomov"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1063/1.533096",
"title": "On the explicit solutions of the elliptic Calogero system",
"url": "https://arxiv.org/abs/solv-int/9905011"
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