The paper asserts a geometric equivalence between the M-CV and 2-mCHE equations via space curve flows, but the derivation is an ansatz and the gauge equivalence is unpublished.
Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries
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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.
fields
nlin.SI 1years
2019 1verdicts
REJECT 1representative citing papers
citing papers explorer
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Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation
The paper asserts a geometric equivalence between the M-CV and 2-mCHE equations via space curve flows, but the derivation is an ansatz and the gauge equivalence is unpublished.