Friday, January 4, 2013

1301.0180 (Changzheng Qu et al.)

Multi-Component Integrable Systems and Invariant Curve Flows in Certain
Geometries
   [PDF]

Changzheng Qu, Junfeng Song, Ruoxia Yao
In this paper, multi-component generalizations to the Camassa-Holm equation, the modified Camassa-Holm equation with cubic nonlinearity are introduced. Geometric formulations to the dual version of the Schr\"odinger equation, the complex Camassa-Holm equation and the multi-component modified Camassa-Holm equation are provided. It is shown that these equations arise from non-streching invariant curve flows respectively in the three-dimensional Euclidean geometry, the two-dimensional M\"obius sphere and $n$-dimensional sphere ${\mathbb S}^n(1)$. Integrability to these systems is also studied.
View original: http://arxiv.org/abs/1301.0180

No comments:

Post a Comment