The meromorphic solutions of the Bruschi-Calogero equation
type: Item
instance of: scholarly article
title: The meromorphic solutions of the Bruschi-Calogero equation
zbMATH Open document ID: 0987.37069
author: Nariya Kawazumi
author: Youichi Shibukawa
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2000-11-09T00:00:00Z
review text: This paper is devoted to the functional equations \[ \alpha(x) \alpha'(y)- \alpha'(x) \alpha(y)= \bigl(\alpha (x+y)-\alpha (x)\alpha(y) \bigr) \bigl(\eta(x) -\eta(y) \bigr), \] which is called the Bruchi-Calogero equation, where the function \(v(x)\) is given by \[ v(x)= {d\over dx}\log \bigl(\alpha (x) \alpha(-x) -1\bigr). \] Note that the Bruchi-Calogero equation is obtained from the Lax representation \(\dot L=[L,M])\) of the equation of motion \[ \ddot q_j= \sum^n_{k=1 \atop k\neq j} \dot q_j\dot q_k v(q_j-q_k),\quad q_j=q_j(t),\;j=1, \dots,n \] which is called Ruijsenaars and Schneider type equation. The authors give all meromorphic solutions of the Bruschi-Calogero equation (1) defined near the origin \(0\in\mathbb{C}\).
Mathematics Subject Classification ID: 37K15
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 35Q58
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 1501167
zbMATH Keywords: Bruschi-Calogero equations
zbMATH Keywords: Lax representation
zbMATH Keywords: functional equation
zbMATH Keywords: meromorphic solution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195143227
OpenAlex ID: W2047026970
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DOI: 10.2977/PRIMS/1195143227
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description: scientific article; zbMATH DE number 1501167