%0 Journal Article
%T Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries
%A Changzheng Qu
%A Junfeng Song
%A Ruoxia Yao
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2013
%I National Academy of Science of Ukraine
%X 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 dinger 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 bius sphere and n-dimensional sphere S^n(1). Integrability to these systems is also studied.
%K invariant curve flow
%K integrable system
%K Euclidean geometry
%K M bius sphere
%K dual Schr dinger equation
%K multi-component modified Camassa-Holm equation
%U http://dx.doi.org/10.3842/SIGMA.2013.001