Notes on Integrable Motion of Two Interacting Curves and Two-layer Generalized Heisenberg Ferromagnet Equations

Akbota Myrzakul; Gulgassyl Nugmanova; Ratbay Myrzakulov; Zhaidary Myrzakulova

arxiv: 1811.12216 · v1 · pith:J6IEQT72new · submitted 2018-11-28 · 🌊 nlin.SI

Notes on Integrable Motion of Two Interacting Curves and Two-layer Generalized Heisenberg Ferromagnet Equations

Zhaidary Myrzakulova , Akbota Myrzakul , Gulgassyl Nugmanova , Ratbay Myrzakulov This is my paper

classification 🌊 nlin.SI

keywords generalizedcurvesequationequationsestablishedferromagnetheisenbergintegrable

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In the present paper, we study the integrable 2-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 2-layer spin system which is the 2-component KdV equation. Finally, the gauge equivalence between these equations is established.

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Notes on Integrable Motion of Two Interacting Curves and Two-layer Generalized Heisenberg Ferromagnet Equations

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