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arXiv · 1812.02152

Integrable Flows of Curves/Surfaces, Generalized Heisenberg Ferromagnet Equation and Complex Coupled Dispersionless Equation

Guldana Bekova·Kuralay Yesmakhanova·Gaukhar Shaikhova·Gulgassyl Nugmanova·Ratbay Myrzakulov
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Abstract

In the present paper, we study the Myrzakulov-XIII (M-XIII) equation geometrically. From the geometric point of view, we establish a link of the M-XIII equation with the motion of space curves in the 3-dimensional space $R^{3}$. We also show that the complex coupled dispersionless (CCD) equation can be derived from the geometrical formalism such that their curve flows are formulated. Finally, the gauge equivalence between the M-XIII equation and the CCD equation is established.

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Guldana Bekova, Kuralay Yesmakhanova, Gaukhar Shaikhova, Gulgassyl Nugmanova, Ratbay Myrzakulov. 2018-12-05. Integrable Flows of Curves/Surfaces, Generalized Heisenberg Ferromagnet Equation and Complex Coupled Dispersionless Equation. https://arxiv.org/abs/1812.02152

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