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arXiv · 2202.00748

Integrable motion of anisotropic space curves and surfaces induced by the Landau-Lifshitz equation

Zh. Myrzakulova·G. Nugmanova·K. Yesmakhanova·R. Myrzakulov
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Abstract

In this paper, we have studied the geometrical formulation of the Landau-Lifshitz equation (LLE) and established its geometrical equivalent counterpart as some generalized nonlinear Schr\"{o}dinger equation. When the anisotropy vanishes, from this result follows the well-known results corresponding for the isotropic case, i.e. to the Heisenberg ferromagnet equation and the focusing nonlinear Schr\"{o}dinger equation. The relations between the LLE and the differential geometry of space curves in the local and nonlocal cases are studied. Using the well-known Sym-Tafel formula, the soliton surfaces induced by the LLE are briefly considered.

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Zh. Myrzakulova, G. Nugmanova, K. Yesmakhanova, R. Myrzakulov. 2022-01-28. Integrable motion of anisotropic space curves and surfaces induced by the Landau-Lifshitz equation. https://arxiv.org/abs/2202.00748

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