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

2013/01/02 by Changzheng Qu, Junfeng Song, Ruoxia Yao
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.DG #math.MP

paper · pdf · doi:10.3842/sigma.2013.001

published as SIGMA 9 (2013), 001, 19 pages

arxiv created 2013/01/02 · arxiv updated 2013/01/03

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 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 \mathbb Sⁿ(1). Integrability to these systems is also studied.

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