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We study noncommutative (NC) field theory of a real NC tachyon and NC U(1)gauge field, describing the dynamics of an unstable D$p$-brane. For every givenset of diagonal component of open string metric $G_{0}$, NC parameter$\theta_{0}$, and interpolating electric field ${\hat E}$, we find all possiblestatic NC kinks as exact solutions, in spite of complicated NC terms, which areclassified by an array of NC kink-antikink and topological NC kinks. Bycomputing their tensions and charges, those configurations are identified as anarray of D0${\bar {\rm D}}$0 and single stable D0 from the unstable D1,respectively. When the interpolating electric field has critical value as$G_{0}^{2}={\hat E}^{2}$, the obtained topological kink becomes a BPS objectwith nonzero thickness and is identified as BPS D0 in the fluid of fundamentalstrings. Particularly in the scaling limit of infinite $\theta_{0}$ andvanishing $G_{0}$ and ${\hat E}$, while keeping $G_{0}\theta_{0}={\hatE}\theta_{0}=1$, finiteness of the tension of NC kink corresponds totensionless kink in ordinary effective field theory. An extension to stableD$(p-1)$ from unstable D$p$ is straightforward for pure electric cases withparallel NC parameter and interpolating two-form field.Comment: 29 pages, references adde

Noncommutative Tachyon Kinks as D(p-1)-branes from Unstable Dp-brane