Non-linear electromagnetic waves in magnetosphere of a magnetar

We compute electromagnetic wave propagation through the magnetosphere of a magnetar. The magnetosphere is modelled as the quantum electrodynamics vacuum and a cold, strongly magnetized plasma. The background field and electromagnetic waves are treated non-perturbatively and can be arbitrarily strong. This technique is particularly useful for examining non-linear effects in propagating waves. Waves travelling through such a medium typically form shocks; on the other hand we focus on the possible existence of waves that travel without evolving. Therefore, in order to examine the non-linear effects, we make a travelling wave ansatz and numerically explore the resulting wave equations. We discover a class of solutions in a homogeneous plasma which are stabilized against forming shocks by exciting non-orthogonal components which exhibit strong non-linear behaviour. These waves may be an important part of the energy transmission processes near pulsars and magnetars.