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arXiv · 1301.0180

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

Changzheng Qu·Junfeng Song·Ruoxia Yao
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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 $n$-dimensional sphere ${\mathbb S}^n(1)$. Integrability to these systems is also studied.

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Changzheng Qu, Junfeng Song, Ruoxia Yao. 2013-01-02. Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries. https://doi.org/10.3842/sigma.2013.001

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