  Bell-Szekeres (BS) solution for colliding electromagnetic waves in
Einstein-Maxwell (EM) theory describes also colliding waves in nonlinear
electrodynamics (NED) with an emergent cosmological constant. Our NED model
covers the first leading orders to the well-known Heisenberg-Euler (HE) type in
a particular gauge of pure magnetic field. Prior to the problem of collision we
obtain dyonic solution for the considered NED theory in a conformally flat
spacetime which has both electric and magnetic fields with constant invariants.
Our sole finding is that null currents inevitably arise in the process of
collision of plane waves in the HE type NED theory.
