Delocalized, non-SUSY $p$-branes, tachyon condensation and tachyon matter

We construct non-supersymmetric $p$-brane solutions of type II supergravities in arbitrary dimensions ($d$) delocalized in one of the spatial transverse directions. By a Wick rotation we convert these solutions into Euclidean $p$-branes delocalized in the transverse time-like direction. The former solutions in $d=10$ nicely interpolate between the $(p+1)$-dimensional non-BPS D-branes and the $p$-dimensional BPS D-branes very similar to the picture of tachyon condensation for the tachyonic kink solution on the non-BPS D-branes. On the other hand the latter solutions interpolate between the $(p+1)$-dimensional non-BPS D-branes and the tachyon matter supergravity configuration very similar to the picture of rolling tachyon on the non-BPS D-branes.