We consider the gauge equivalence of all NLS-type reductions with a coupled system of Landau–Lifshitz equations. In the local case it is shown to reduce to the continuum limit of the classical isotropic Heisenberg ferromagnet equation. All nonlocal reductions, however, are shown to be equivalent to a two-sublattice antiferromagnetic system. Nonlocal solitons are shown to represent excitations from nonzero ground state magnetization and antiferromagnetic vectors, indicative of a ferrimagnetic system. An alternate geometric interpretation is given by means of a coupled Hasimoto transformation, establishing the connection between the nonlocal reductions of the AKNS system and the motion of a curve in ${ℂ}^3$. Through Darboux transformations, the one-soliton solutions of the coupled LL equations are obtained.

我们考虑用Landau–Lifshitz方程的耦合系统来考虑所有NLS型归约的规范当量。在局部情况下，它可以减小到经典的各向同性海森堡铁磁体方程的连续极限。然而，所有的非局部减少都显示为等效于两个子格的反铁磁系统。示出了非局部孤子表示来自非零基态磁化强度和反铁磁矢量的激励，这表示亚铁磁系统。通过耦合的Hasimoto变换给出了另一种几何解释，该变换在AKNS系统的非局部归约与曲线运动之间建立了联系。${ℂ}^3$。通过Darboux变换，获得了耦合LL方程的单孤子解。