×

Existence of standing pulse solutions to an inhomogeneous reaction-diffusion system. (English) Zbl 0896.34041

Summary: 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.

MSC:

34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
35K57 Reaction-diffusion equations
34E15 Singular perturbations for ordinary differential equations
78A60 Lasers, masers, optical bistability, nonlinear optics
PDFBibTeX XMLCite
Full Text: DOI