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October  2004, 10(4): 857-869. doi: 10.3934/dcds.2004.10.857

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, United States
2. 

Department of Mathematics, The Ohio State University, Columbus, OH 43210, United States

Received  December 2002 Revised  October 2003 Published  March 2004

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: resonances., Evans function.
Mathematics Subject Classification: 34A26, 34C35, 34C37, 35K57, 35P1.
Citation: Todd Kapitula, Björn Sandstede. Eigenvalues and resonances using the Evans function. Discrete & Continuous Dynamical Systems, 2004, 10 (4) : 857-869. doi: 10.3934/dcds.2004.10.857
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