Properties of modified plasma waves in non-linear electrodynamics are investigated. We consider a cold, uniform, collisionless, and magnetized plasma model. Initially, we also assume small amplitude waves and the non-relativistic approximation. For electrostatic waves, we obtain a modified Trivelpiece–Gould dispersion relation with a suitable change in the plasma frequency and analyze the stability of modes. Furthermore, electromagnetic waves related to the generalized Appleton–Hartree equation are established. In this case, we discuss modifications in circularly polarized waves and ordinary and extraordinary modes. After that, we apply our results to particular cases of low-energy quantum electrodynamics and a generalized Born–Infeld model. The correspondent dispersion relations and effects on the propagation regions are determined. Finally, we include the relativistic and large amplitude effects for circularly polarized waves. We obtain the dispersion relation within effective non-linear electrodynamics and examine the behavior of the refractive index when the frequency of the propagating wave converges to the plasma frequency.

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