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Alfven Mach number Alfven speed c/cope characteristic soliton width cold plasma model component of Eq.(12 continuity equation dB/dx dS/dxi effects become important electric potential electron component electron fluid velocity electron inertial length electron velocity vye exceed the speed Field Yukiharu OHSAWA final speed fluid electron velocity form similar given by10 highly relativistic ion and electron K-dV equation Magnetic Field Yukiharu magnetosonic soliton magnetosonic wave propagating Maxwell's equations Nagoya University non-relativistic theory breaks non-relativistic two-fluid nonlinear fast magnetosonic nonlinear magnetosonic wave nonlinear wave parameter regime particle motion perpendicular magnetosonic wave plasma parameters Plasma Physics quasi-perpendicular regions relativistic effects become relativistic gamma Relativistic Magnetosonic Wave relativistic theory relativistic two-fluid cold resonant ions resonantly accelerated ions scale length shock waves shown solitary wave solution speed of light stationary nonlinear wavetrain stationary solitary wave stationary solutions trapped ions two-fluid cold plasma vye is plotted wave front wave propagating perpendicularly wave-amplitude wave-frame zero 3 plasma