We establish first-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The potential is allowed to depend arbitrarily on both variables. The systems we consider here include the scenario of a position-dependent mass as well as the massless case. Our Darboux transformations are more general than their existing counterparts (Pozdeeva and Schulze-Halberg in J Math Phys 51:113501, 2010).

中文翻译：

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二维任意对角势矩阵狄拉克方程的一阶达布变换

我们为具有对角矩阵势的二维狄拉克方程建立一阶 Darboux 变换。允许势任意取决于两个变量。我们在这里考虑的系统包括依赖位置的质量和无质量情况。我们的 Darboux 变换比它们现有的变换更通用（Pozdeeva 和 Schulze-Halberg in J Math Phys 51:113501, 2010）。