Relativistic solitons in pulsar wind nebulae

The conversion mechanisms responsible for the transformation of the relativistic stellar wind to the observed pulsar nebula electromagnetic radiation is one of the most interesting problems of the high energy astrophysics. In particular, the existence of a connection between the giant flares of the gamma-radiation from the Crab nebula (which were discovered in 2011 by Fermi and AGILE telescopes) and observed dynamical structures remains being a question. To address the origin of the observed dynamical structures in the shocked wind we consider here a model of a weak nonlinear perturbation propagating transverse to the mean quasi-stationary magnetic field in the pulsar nebula plasma. The plasma is supposed to be electron-positron and relativistic. It is shown that in the regime of the strong scattering of pairs by the stochastic magnetic field fluctuation the propagation of magnetic field perturbation can be described by well-known Korteweg — de Vries (KdV) equation. One of the KdV solutions is a soliton — a long lived solitary wave, propagating without changing of its shape. The width of plasma magnetic soliton in the presence of ultra-relativistic pairs is discussed.