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Nonlinear Electromagnetic Waves in Magnetosphere of a Magnetar

We compute electromagnetic wave propagation through the magnetosphere of a magnetar. The magnetosphere is modeled as the QED vacuum and a cold, strongly magnetized plasma. The background field and electromagnetic waves are treated nonperturbatively 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 nonlinear 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 nonorthogonal components which exhibit strong nonlinear behaviour. These waves may be an important part of the energy transmission processes near pulsars and magnetars.