Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries
Exactly Solvable and Integrable Systems
2013-01-03 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
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 -dimensional sphere . Integrability to these systems is also studied.
Cite
@article{arxiv.1301.0180,
title = {Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries},
author = {Changzheng Qu and Junfeng Song and Ruoxia Yao},
journal= {arXiv preprint arXiv:1301.0180},
year = {2013}
}