ar X iv : h ep - t h / 00 05 16 5 v 1 1 8 M ay 2 00 0 D – Branes and their Absorptivity in Born – Infeld Theory

Standard methods of nonlinear dynamics are used to investigate the stability of particles, branes and D-branes of abelian Born–Infeld theory. In particular the equation of small fluctuations about the D–brane is derived and converted into a modified Mathieu equation and – complementing earlier low–energy investigations in the case of the dilaton–axion system – studied in the high–energy domain. Explicit expressions are derived for the S–matrix and absorption and reflection amplitudes of the scalar fluctuation in the presence of the D-brane. The results confirm physical expectations and numerical studies of others. With the derivation and use of the (hitherto practically unknown) high energy expansion of the Floquet exponent our considerations also close a gap in earlier treatments of the Mathieu equation.