The paper discusses the Nonlinear Dirac Equation with Kerr-type nonlinearity (i.e., $\psi^{p-2}\psi$) on noncompact metric graphs with a finite number of edges, in the case of Kirchhoff-type vertex conditions. Precisely, we prove local well-posedness for the associated Cauchy problem in the operator domain and, for infinite $N$-star graphs, the existence of standing waves bifurcating from the trivial solution at $\omega=mc^2$, for any $p>2$. In the Appendix we also discuss the nonrelativistic limit of the Dirac-Kirchhoff operator.

中文翻译：

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关于非紧度量图上的非线性狄拉克方程

该论文讨论了在基尔霍夫型顶点条件的情况下，具有有限边数的非紧度量度图上的具有克尔型非线性（即 $\psi^{p-2}\psi$）的非线性狄拉克方程。准确地说，我们证明了算子域中相关柯西问题的局部适定性，并且对于无限的 $N$-星图，存在从 $\omega=mc^2$ 处的平凡解分叉的驻波，对于任何$p>2$。在附录中，我们还讨论了 Dirac-Kirchhoff 算子的非相对论极限。