Solitary wave of ground state type for a nonlinear Klein–Gordon equation coupled with Born–Infeld theory in $\mathbb{R}^{2}$

In this paper we prove the existence of nontrivial ground state solution for a nonlinear Klein–Gordon equation coupled with Born–Infeld theory in $\mathbb{R}^{2}$ involving unbounded or decaying radial potentials. The approach involves variational methods combined with a Trudinger–Moser type inequality and a symmetric criticality type result.