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The two-dimensional problem for double simple waves in an
electronpositron plasma is analytically solved. The relations
between the hydrodynamical quantities and two components of the
wave velocity are found. For explicit description of spatial and
time behavior of quantities, the initial distributions (for
instance of the velocity) must be known. The initial distributions
must satisfy a definite condition, which means that the double
simple wave cannot be developed from every initial condition. As
in the usual simple wave, the two-dimensional double simple wave
can suffer discontinuities during its evolution. An equation for
the characteristic surface (characterizing the propagation of
disturbances under the double simple wave restriction) is
constructed. It is also shown that in the two-dimensional case it
is impossible to find any Riemann invariant.
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