We introduce the theory of optical spherical Heisenberg ferromagnetic spin of timelike spherical normal magnetic flows of particles by the spherical frame in de Sitter space. Also, the concept of timelike spherical normal magnetic particles is investigated, which may have evolution equations. Afterward, we reveal new relationships with some integrability conditions for timelike spherical normal magnetic flows in de-Sitter space. In addition, we obtain total phases for spherical normal magnetic flows. We also acquire perturbed solutions of the nonlinear Schrödinger's equation that governs the propagation of solitons in de-Sitter space ${\mathbb{S}}_1^2$. Finally, we provide some numerical simulations to supplement the analytical outcomes.

我们通过de Sitter空间中的球面框架介绍了时空球面法向磁流的光学球面海森堡铁磁自旋理论。此外，研究了时态球形法向磁性粒子的概念，它可能具有演化方程。随后，我们揭示了与De-Sitter空间中类似时间的球形法向磁流有关的一些可积分条件的新关系。此外，我们获得了球形法向磁流的总相位。我们还获得了控制De-Sitter空间中孤子传播的非线性Schrödinger方程的摄动解${\mathbb{小号}}_{\mathrm{1个}}^2$。最后，我们提供一些数值模拟以补充分析结果。