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

Changzheng Qu ; Junfeng Song ; Ruoxia Yao

Symmetry, integrability and geometry: methods and applications, Tome 9 (2013)

Résumé

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 ${\mathbb S}^n(1)$. Integrability to these systems is also studied.

Détail

Keywords: invariant curve flow; integrable system; Euclidean geometry; Möbius sphere; dual Schrödinger equation; multi-component modified Camassa–Holm equation.

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