Kinks of open superstring field theory

We construct approximate kink solutions of supersymmetric open string field theory at lowest level when non-local operators in the tachyon effective action are fully taken into account. To this purpose we derive two duplication formulæ for products of incomplete gamma functions, which determine the level of approximation of the solutions. The time kink is an instanton of the Euclidean theory with a well-defined tunneling probability. The spatial kink solution represents an unstable D9-brane decaying into a stable D8-brane. We calculate the ratio of the brane tensions, which almost exactly reproduces the expected value.