Quasi-parallel propagating solitons in magnetised relativistic electron-positron plasmas

In this article, we study nonlinear waves propagating along the background magnetic field in relativistic electron-positron plasmas. Using the reductive perturbation method, we derive a three-dimensional equation describing these waves. When the perturbations do not vary in the directions orthogonal to the background magnetic field this equation reduces to the vector modified Kortewed-de Vries equation. We present solutions of the obtained equation in the form of planar solitary waves and describe the results of study of their stability with respect to transverse perturbations. We also study numerically non-planar solitary waves.