In this study, we study optical hasimoto map corresponds to under the quasi-frame for timelike curves in 3D Minkowski space. We investigate the relationship of this transformation with some flow equations, which are known examples for nonlinear optical systems. Here, we first obtain the $q$-Hasimoto map as equivalent of the Hasimoto map in the $q$-frame for timelike space curve in 3D Minkowski Space. Then, we examine the effect on the $q$-Hasimoto map of the some flow equations such as vortex filament equation, Heisenberg antiferromagnetic flow. Finally, we present comments on some of the physical consequences of these effects that we have examined.

在这项研究中，我们研究了光学 hasimoto 映射对应于 3D Minkowski 空间中类时曲线的准框架下。我们研究了这种变换与一些流动方程的关系，这些方程是非线性光学系统的已知例子。在这里，我们首先得到$q$-Hasimoto 地图相当于 Hasimoto 地图中的 $q$- 3D Minkowski 空间中类时空间曲线的框架。然后，我们检查对$q$- 涡丝方程、海森堡反铁磁流等一些流动方程的Hasimoto图。最后，我们对我们研究过的这些影响的一些物理后果发表评论。