An Explicit Theory for Pulses in Two Component, Singularly Perturbed, Reaction–Diffusion Equations

摘要: In recent years, methods have been developed to study the existence, stability and bifurcations of pulses in singularly perturbed reaction–diffusion equations one space dimension, context a number explicit model problems, such as Gray–Scott Gierer–Meinhardt equations. Although these are principle general nature, their applicability priori relies on characteristics models. For instance, slow reduced spatial problem is linear models considered literature. Moreover, nonlinearities fast very specific, polynomial, nature. These properties crucially used, especially bifurcation analysis. this paper, we present an theory for two-component that significantly extends generalizes existing methods.