We obtain an exact spherically symmetric and magnetically charged black hole solution in 4D Einstein$-$Gauss$-$Bonnet gravity coupled with nonlinear electrodynamics with the Lagrangian ${\mathcal{L}}_{NED}=-\mathcal{F}∕(1+\sqrt{2\mid \beta \mathcal{F}\mid })$ ($\mathcal{F}$ is the field strength invariant). The thermodynamics of the black hole is studied within our model. We calculate the Hawking temperature and the heat capacity of the black hole. The phase transitions occur in the point where the Hawking temperature possesses an extremum and the heat capacity diverges. It was shown that black holes are thermodynamically stable in some range of event horizon radii when the heat capacity and Hawking temperature are positive. The logarithmic correction to the Bekenstein$-$Hawking BH entropy is obtained which mimics a quantum correction. The dependence of the BH shadow radius on the model parameters is studied. We also investigate the particle emission rate of the BH. The stability of the BH is studied by analysing the quasinormal modes.

我们在4D爱因斯坦中获得精确的球对称和带电黑洞解$-$高斯$-$阀盖重力与拉格朗日非线性电动力学耦合 ${\mathcal{大号}}_{ñEd}=-\mathcal{F}∕（\mathrm{1个}+\sqrt{\mathrm{2个}\mid \beta \mathcal{F}\mid }）$ （$\mathcal{F}$是场强不变的）。在我们的模型中研究了黑洞的热力学。我们计算霍金温度和黑洞的热容。相变发生在霍金温度达到极值且热容发散的点上。结果表明，当热容和霍金温度为正值时，黑洞在事件视界半径的一定范围内是热力学稳定的。Bekenstein的对数校正$-$获得模仿量子校正的霍金BH熵。研究了BH阴影半径对模型参数的依赖性。我们还研究了BH的颗粒发射率。通过分析准正态模研究了BH的稳定性。