  We find exact tachyon kink solutions of DBI type effective action describing
an unstable D5-brane with worldvolume gauge field turned on in a curved
background. The background of interest is the ten-dimensional lift of the
Salam-Sezgin vacuum and, in the asymptotic limit, it approaches ${\rm
R}^{1,4}\times {\rm T}^2\times {\rm S}^3$. The solutions are identified as
composites of lower-dimensional D-branes and fundamental strings, and, in the
BPS limit, they become a D4D2F1 composite wrapped on ${\rm R}^{1,2}\times {\rm
T}^2$ where ${\rm T}^2$ is inside ${\rm S}^3$. In one class of solutions we
find an infinite degeneracy with respect to a constant magnetic field along the
direction of NS-NS field on ${\rm S}^3$.
