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.
Borrelli, W., Symmetric Solutions for a 2D Critical Dirac Equation, <<COMMUNICATIONS IN CONTEMPORARY MATHEMATICS>>, N/A; (N/A): N/A-N/A. [doi:10.1142/S021919972150019X] [http://hdl.handle.net/10807/171305]
Symmetric Solutions for a 2D Critical Dirac Equation
Borrelli, William
2021
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 also prove smoothness and exponential decay at infinity.
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