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A two-dimensional double simple wave solution is given for both weakly and highly magnetized
non-relativistic plasmas moving across the magnetic field. The dependence of the
density and the magnetic field on the two independent phases, namely, components of the
fluid velocity is derived. It is shown that initial spatial distributions must satisfy a definite
equation whose solution determines a special category for initial conditions. The time of
blow up for any fixed value of the pair phase is found. A large general class of solutions for
initial distributions is obtained. For any chosen initial distribution, the physical plane of
flow at any instant of time splits into two regions, one forbidden and the other permitted.
These regions are obtained numerically at a typical time for a special initial distribution.
For this double wave solution, differential equations for streamlines and fluid trajectories
are derived. Only for simplest cases the corresponding curves can be completely integrated
and are given in the paper.
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