A detailed study has been carried out on the propagation of a solitary wave along the magnetic field in a cold collision-free plasma. With the quasi-neutral approximation and the conservation of momentum flux and energy flux in the wave-frame, the exact analytical solutions of the stationary solitary pulse in terms of particle densities, parallel and transverse velocities, and transverse magnetic fields are presented without performing numerical integration. Graphical representations of the solutions and in particular the 3D structures of the transverse magnetic and velocity field lines are presented.

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