Electromagnetic solitons in quantum vacuum

In the limit of extremely intense electromagnetic fields the Maxwell equations are modified due to the photon-photon scattering that makes the vacuum refraction index depend on the field amplitude. In the presence of electromagnetic waves with small but finite wave numbers the vacuum behaves as a dispersive medium. We show that the interplay between the vacuum polarization and the nonlinear effects in the interaction of counter-propagating electromagnetic waves can result in the formation of Kadomtsev-Petviashvily solitons and, in one-dimension configuration, of Korteveg-de-Vries type solitons that can propagate over a large distance without changing their shape.