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arXiv · 2004.12816

Zakharov-Ito equation and Generalized Heisenberg ferromagnet-type equation: equivalence and related geometric curve flows

Zhanbala Umbetova·Shynaray Myrzakul·Kuralay Yesmakhanova·Tolkynay Myrzakul·Gulgassyl Nugmanova·Ratbay Myrzakulov
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Abstract

These results continue our studies of integrable generalized Heisenberg ferromagnet-type equations (GHFE) and their equivalent counterparts. We consider the GHFE which is the spin equivalent of the Zakharov-Ito equation (ZIE). We have established that these equations are gauge and geometrical equivalent to each other. The integrable motion of space curves induced by the ZIE is constructed. The 1-soliton solution of the GHFE is obtained from the seed solution of the ZIE.

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Zhanbala Umbetova, Shynaray Myrzakul, Kuralay Yesmakhanova, Tolkynay Myrzakul, Gulgassyl Nugmanova, Ratbay Myrzakulov. 2020-04-23. Zakharov-Ito equation and Generalized Heisenberg ferromagnet-type equation: equivalence and related geometric curve flows. https://arxiv.org/abs/2004.12816

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