Oblique solitary Alfvén modes in relativistic electron-positron plasmas

TLDR: The nonlinear evolution of a generalized X-mode is governed by a Korteweg-de Vries equation, valid at all angles of propagation except strictly parallel propagation, for which a different approach had been given already as discussed by the authors.

Abstract: In electron-positron plasmas the charge-to-mass ratio is the same for both species. This leads for different waves to the vanishing of certain coefficients in the dispersion laws and nonlinear evolution equations, and also to the decoupling of some of the plasma modes. In particular, there is a low-frequency mode which exists at all angles of propagation with respect to the static magnetic field, corresponding at parallel propagation to a degenerate case of circularly polarized waves, and at perpendicular propagation to part of the extraordinary mode. The nonlinear evolution of this generalizedX-mode is governed by a Korteweg-de Vries equation, valid at all angles of propagation except strictly parallel propagation, for which a different approach had been given already. The nonlinearity is strongest at perpendicular propagation.