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A multi-dimensional simple wave formalism is employed to obtain a
2-D quasi-simple wave for a weakly dissipative fluid. This is the
natural but nontrivial generalization of the so called
unidirectional quasi-simple wave. The nonlinearity as well as the
smallness of quantities is taken up to second order leading to a
2-D Burgers equation for the wave phase. Five different solutions
are discussed. Two of them are traveling waves with arbitrary
directions whose passage may both increase or decrease the fluid
parameters. Other two solutions have moving lines of Gaussian
localizations with fined directions. In one of these two, the
fluid variables will go to non-equilibrium limits while in the
other they decay to the equilibrium. The fifth solution indicates
a moving-decaying triangular shock structure.
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