  We search for exact tachyon kink solutions of DBI type effective action
describing an unstable D-brane with worldvolume gauge field turned in both the
flat and a curved background. There are various kinds of solutions in the
presence of electromagnetic fields in the flat space, such as periodic arrays,
topological tachyon kinks, half kinks, and bounces. We identify a BPS object,
D($p$-1)F1 bound state, which describes a thick brane with string flux density.
The curved 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 in the curved
background 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 ${\rm
S}^3$.
