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

2020/04/23 by Zhanbala Umbetova, Shynaray Myrzakul, Umbetova, Zhanbala +9
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2004.12816

openalex publication_date 2020/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Darboux transformations and exact soliton solutions of integrable coupled spin systems related with the Manakov system
• Integrable Motion of Curves, Spin Equation and Camassa-Holm Equation

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