In this paper, we show the existence of infinitely many symmetric solutions for a cubic Dirac equation in two dimensions, which appears as effective model in systems related to honeycomb structures. Such equation is critical for the Sobolev embedding and solutions are found by variational methods. Moreover, we also prove smoothness and exponential decay at infinity.

中文翻译：

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二维临界狄拉克方程的对称解

在本文中，我们展示了二维三次狄拉克方程的无限多个对称解的存在，这在与蜂窝结构相关的系统中显示为有效模型。这样的方程对于 Sobolev 嵌入至关重要，并且可以通过变分方法找到解决方案。此外，我们还证明了无穷远处的平滑度和指数衰减。