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

Autor:	Myrzakulova, Zh., Nugmanova, G., Yesmakhanova, K., Myrzakulov, R.
Rok vydání:	2022
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
Popis:	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. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.00748 Zobrazit plný text záznamu View this record from Arxiv