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Erschienen in:
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2013 | OriginalPaper | Buchkapitel

10. The Evans Function for nth-Order Operators on the Real Line

verfasst von : Todd Kapitula, Keith Promislow

Erschienen in: Spectral and Dynamical Stability of Nonlinear Waves

Verlag: Springer New York

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Abstract

The primary goal of this chapter is the construction of the Evans function for eigenvalue problems associated with nth-order, exponentially asymptotic linear operators acting on L2(R). The construction, through the Jost solutions, is distinguished from the construction for second-order operators by the fact that the matrix eigenvalues and associated eigenvectors for the nth-order problem may not be analytic in the natural domain of the Evans function. Moreover, while it is relatively easy to determine the essential spectrum for these problems, the matrix eigenvalues and the absolute spectrum do not generally have an explicit representation. We sidestep these issues via an analytic extension of the stable and unstable spaces of the asymptotic matrix which leads to the construction of Jost matrices.

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Vorheriges Kapitel The Evans Function for Sturm–Liouville Operators on the Real Line
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Metadaten
Titel
The Evans Function for nth-Order Operators on the Real Line
verfasst von
Todd Kapitula
Keith Promislow
Copyright-Jahr
2013
Verlag
Springer New York
Buch
Spectral and Dynamical Stability of Nonlinear Waves

Print ISBN: 978-1-4614-6994-0

Electronic ISBN: 978-1-4614-6995-7

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4614-6995-7_10