Symmetric solutions for a 2D critical Dirac equation

TL;DR

This paper proves the existence of infinitely many symmetric solutions for a critical 2D Dirac equation related to honeycomb structures, using variational methods, and establishes their smoothness and exponential decay.

Contribution

It introduces new symmetric solutions for a critical 2D Dirac equation and demonstrates their properties, advancing understanding of such equations in physical models.

Findings

Infinitely many symmetric solutions exist for the 2D critical Dirac equation.

Solutions are smooth and decay exponentially at infinity.

Variational methods are effective for finding solutions in critical Sobolev settings.

Abstract

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 prove also prove smoothness and exponential decay at infinity.