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arXiv · 1908.01371

Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation

Bayan Kutum·Gulgassyl Nugmanova·Tolkynay Myrzakul·Kuralay Yesmakhanova·Ratbay Myrzakulov
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Abstract

In this paper, we provide the geometric formulation to the two-component Camassa-Holm equation (2-mCHE). We also study the relation between the 2-mCHE and the M-CV equation. We have shown that these equations arise from the invariant space curve flows in three-dimensional Euclidean geometry. Using this approach we have established the geometrical equivalence between the 2-mCHE and the M-CV equation. The gauge equivalence between these equations is also considered.

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Bayan Kutum, Gulgassyl Nugmanova, Tolkynay Myrzakul, Kuralay Yesmakhanova, Ratbay Myrzakulov. 2019-08-04. Integrable Deformation of Space Curves, Generalized Heisenberg Ferromagnet Equation and Two-Component Modified Camassa-Holm Equation. https://arxiv.org/abs/1908.01371

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