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