It is shown that first-order Darboux transformations for the two-dimensional massless Dirac equation with scalar potential and for the Schrödinger equation are the same up to a change of coordinates. As a consequence, we obtain a closed-form representation of iterated, higher-order Darboux transformations for our Dirac equation. We use the formalism to generate several new exactly-solvable Dirac systems through higher-order Darboux transformations.

中文翻译：

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无质量 Dirac 方程的迭代 Darboux 变换的闭式表示

结果表明，具有标量势的二维无质量狄拉克方程和薛定谔方程的一阶达布变换在坐标变化之前是相同的。因此，我们为我们的狄拉克方程获得了迭代的、高阶 Darboux 变换的封闭形式表示。我们使用形式主义通过高阶 Darboux 变换生成几个新的完全可解的 Dirac 系统。