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Abstract and Applied Analysis
Volume 2014, Article ID 275450, 8 pages
http://dx.doi.org/10.1155/2014/275450
Research Article

Consecutive Rosochatius Deformations of the Garnier System and the Hénon-Heiles System

School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China

Received 8 January 2014; Accepted 20 February 2014; Published 31 March 2014

Academic Editor: Weiguo Rui

Copyright © 2014 Baoqiang Xia and Ruguang Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An algorithm of constructing infinitely many symplectic realizations of generalized sl(2) Gaudin magnet is proposed. Based on this algorithm, the consecutive Rosochatius deformations of integrable Hamiltonian systems are presented. As examples, the consecutive Rosochatius deformations of the Garnier system and the Hénon-Heiles system as well as their Lax representations, are obtained.