Oblique solitons in a cold magnetized plasma

A fully nonlinear theory for stationary waves, propagating obliquely to the ambient magnetic field in a cold plasma, has been developed. Soliton solutions, representing both compressions and rarefactions in the magnetic field, exist for sub-fast flow conditions and in certain cones of magnetic obliquity. The soliton is explicitly characterized, in terms of the wave speed and its obliquity, by a parameter m (the “soliton number”). Compressive (“bright”) solitons are found to have a maximum attainable compression amplitude of three, corresponding to the condition m=1. Rarefactive (“dark”) solitons attain complete rarefaction when m=4. The properties of these stationary waves are described both in terms of magnetic hodographs, and of a spatial structure equation, whose equilibrium points yield the maximum compression and rarefaction at the center of the waves. An analytic solution, in terms of elementary transcendental functions, is also presented and highlights the role played by the soliton number m in determining the speed, strength and width of the solitons.