论文标题
Landau-Lifshitz方程引起的各向异性空间曲线和表面的可整合运动
Integrable motion of anisotropic space curves and surfaces induced by the Landau-Lifshitz equation
论文作者
论文摘要
在本文中，我们研究了Landau-Lifshitz方程（LLE）的几何表述，并确立了其几何等效物作为某些广义的非线性Schrödinger方程。当各向异性消失时，从这个结果消失了，遵循众所周知的结果对应于各向同性情况，即与海森伯格·弗罗格内特方程和聚焦的非线性schrödinger方程相对应。研究了LLE与局部和非局部病例中空间曲线的差异几何形状之间的关系。使用众所周知的符号公式，简要考虑由LLE诱导的孤子表面。
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 Schrödinger 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 Schrödinger 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.
