Existence of standing pulse solutions to an inhomogeneous reaction-diffusion system

We prove the existence of locally unique, symmetric standing pulse solutions to homogeneous and inhomogeneous versions of a certain reaction-diffusion system. This system models the evolution of photoexcited carrier density and temperature inside the cavity of a semiconductor Fabry-Pérot interferometer. Such pulses represent the fundamental nontrivial mode of pattern formation in this device. Our results follow from a geometric singular perturbation approach, based largely on Fenichel's theorems and the Exchange Lemma. © 1998 Plenum Publishing Corporation.