Notes on integrable motion of two interacting curves and two-layer generalized Heisenberg ferromagnet equations
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We study the integrable two-layer generalized Heisenberg ferromagnet equation (HFE). The relation between this generalized HFE and differential geometry of curves is established. Using this relation we found the geometrical equivalent counterpart of the two-layer spin system which is the two-component KdV equation. Finally, the gauge equivalence between these equations is established.
Keywordstwo-layer spin system two interacting curves gauge equivalence
Mathematics Subject Classification (2000)Primary 53C05 Secondary 53C35
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