Spectra and Stability of Spatially Periodic Pulse Patterns: Evans Function Factorization via Riccati Transformation

In the spectral stability analysis of localized patterns to singular perturbed evolution problems, one often encounters that the Evans function respects the scale separation. In such cases the Evans function of the full linear stability problem can be approximated by a product of a slow and a fast reduced Evans function, which correspond to properly scaled slow and fast singular limit problems. This feature has been used in several spectral stability analyses in order to reduce the complexity of the linear stability problem. In these studies the factorization of the Evans function was established via geometric arguments that need to be customized for the specific equations and solutions under consideration. In this paper we develop an alternative factorization method. In this analytic method we use the Riccati transformation and exponential dichotomies to separate slow from fast dynamics. We employ our factorization procedure to study the spectra associated with spatially periodic pu...

• Type: Journal
• Year: 2016
• Where: SIAMMA
• Authors: Björn de Rijk, Arjen Doelman, Jens D. M. Rademacher
• Keywords: Computer Graphics, SIAMMA 2016