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

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arxiv 2004.12816 v1 pith:SLJ3AST5 submitted 2020-04-23 nlin.SI

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

classification nlin.SI
keywords equationequivalentghfeequationsferromagnet-typegeneralizedheisenbergintegrable
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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