  We construct time dependent BPS pp-wave brane solutions in the context of
M-theory and type II supergravity. It is found that N-brane solutions we
considered satisfy the crossing rule as S-brane solutions but 1/8 supersymmetry
remains. By applying them to the cosmological setting, inflationary solutions
are obtained. During this inflation, the size of the extradimensions becomes
smaller than our four-dimensional spacetime dynamically. We also discuss the
mechanism for terminating this inflation and recovering the hot big-bang
universe.
