Eigenvalues and resonances using the Evans function

Todd Kapitula; Björn Sandstede

doi:10.3934/dcds.2004.10.857

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2004, Volume 10, Issue 4: 857-869. Doi: 10.3934/dcds.2004.10.857

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Eigenvalues and resonances using the Evans function

Todd Kapitula^1, and
Björn Sandstede^2,

1.
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87111
2.
Department of Mathematics, The Ohio State University, Columbus, OH 43210

Received: November 30, 2002

Revised: September 30, 2003

Published: September 2004

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Abstract

In this expository paper, we discuss the use of the Evans function in finding resonances, which are poles of the analytic continuation of the resolvent. We illustrate the utility of the general theory developed in [13, 14] by applying it to two physically interesting test cases: the linear Schrödinger operator and the linearization associated with the integrable nonlinear Schrödinger equation.

Keywords:

Evans function,
resonances.

Mathematics Subject Classification: 34A26, 34C35, 34C37, 35K57, 35P15.

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