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

Symmetry Integrability and Geometry-Methods and Applications

article

Changzheng Qu¹  Junfeng Song²  Ruoxia Yao³ 

[1] Center for Nonlinear Studies, Ningbo University;College of Mathematics and Information Science, Shaanxi Normal University;School of Computer Science, Shaanxi Normal University

关键词: invariant curve flow;    integrable system;    Euclidean geometry;    M¨obius sphere;    dual Schr¨odinger equation;    multi-component modified Camassa–Holm equation;   

DOI  :  10.3842/SIGMA.2013.001

来源: National Academy of Science of Ukraine

【 摘 要 】

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 Schrödinger 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 Möbius sphere and n -dimensional sphere S n (1). Integrability to these systems is also studied.

【 授权许可】

Unknown