Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries
نویسندگان
چکیده
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 ndimensional sphere S(1). Integrability to these systems is also studied.
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