In this paper, we introduce new frame and new transformation associated with combined Korteweg–de Vries–modified Korteweg–de Vries (KdV–mKdV) equation, the mKdV and the KdV equations with respect to the null Cartan frame in Minkowski 3-space. Direction of the state of polarization of monochromatic linear polarized light wave traveling in the optic fiber is given by the direction of electric field vector. We show that the electric field vector E⃗ can be expressed as a linear combination of null Cartan frame apparatus using this new transformation in Minkowski 3-space. Later, we study rotation of the polarization plane along optic fiber according to null Cartan frame and Frenet frame of pseudo-null curve in Minkowski 3-space. Finally, we obtain Lorentz force equations via null and pseudo null electromagnetic curves.

中文翻译：

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零嘉当框架和伪零框架沿光纤的电场变化

在本文中，我们介绍了与组合 Korteweg-de Vries-modified Korteweg-de Vries (KdV-mKdV) 方程、mKdV 和 KdV 方程相关的新框架和新变换，这些方程与 Minkowski 3 空间中的零 Cartan 框架有关。在光纤中传播的单色线偏振光波的偏振态方向由电场矢量的方向给出。我们证明了电场矢量乙⃗可以表示为在 Minkowski 3 空间中使用这种新变换的零嘉当框架装置的线性组合。之后，我们根据Minkowski 3空间中伪零曲线的零Cartan框架和Frenet框架研究了偏振面沿光纤的旋转。最后，我们通过零和伪零电磁曲线获得洛伦兹力方程。