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Quasi-parallel propagation of solitary waves in magnetised non-relativistic electron–positron plasmas

We study the propagation of nonlinear waves in non-relativistic electron–positron plasmas. The waves are assumed to propagate at small angles with respect to the equilibrium magnetic field. We derive the equation describing the wave propagation under the assumption that the waves are weakly dispersive and also can weakly depend on spatial variables orthogonal to the equilibrium magnetic field. We obtain solutions of the derived equation describing solitons. Then we study the stability of solitons with respect to transverse perturbations.