期刊
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
卷 2012, 期 13, 页码 3089-3125出版社
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rnr120
关键词
-
类别
资金
- Universidad Politecnica de Madrid [AL07-PID-056, AL08-PID-49]
- Fondo Nacional de Desarrollo Cientifico y Tecnologico (FONDECYT) [1070191]
- Research Ring Anillo Ecuaciones Asociadas a Reticulados
- World Bank
It is known that the Camassa-Holm (CH) equation describes pseudo-spherical surfaces and that therefore its integrability properties can be studied by geometrical means. In particular, the CH equation admits nonlocal symmetries of pseudo-potential type: the standard quadratic pseudo-potential associated with the geodesics of the pseudo-spherical surfaces determined by (generic) solutions to CH, allows us to construct a covering pi of the equation manifold of CH on which nonlocal symmetries can be explicitly calculated. In this article, we present the Lie algebra of (first-order) nonlocal pi-symmetries for the CH equation, and we show that this algebra contains a semidirect sum of the loop algebra over sl(2,R) and the centerless Virasoro algebra. As applications, we compute explicit solutions, we construct a Darboux transformation for the CH equation, and we recover its recursion operator. We also extend our results to the associated Camassa-Holm equation introduced by J. Schiff.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据