On the spectrum of the superposition of separated potentials.

J. Douglas Wright

doi:10.3934/dcdsb.2013.18.273

Article Contents

2013, Volume 18, Issue 1: 273-281. Doi: 10.3934/dcdsb.2013.18.273

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On the spectrum of the superposition of separated potentials.

J. Douglas Wright^1,

1.
Drexel University, Department of Mathematics, 3141 Chestnut Ave, Philadelphia, PA 19104

Received: March 31, 2012

Revised: June 30, 2012

Published: December 2012

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Abstract

Suppose that $V(x)$ is an exponentially localized potential and $L$ is a constant coefficient differential operator. A method for computing the spectrum of $L+V(x-x_1) + ... + V(x-x_N)$ given that one knows the spectrum of $L+V(x)$ is described. The method is functional theoretic in nature and does not rely heavily on any special structure of $L$ or $V$ apart from the exponential localization. The result is aimed at applications involving the existence and stability of multi-pulses in partial differential equations.

Keywords:

Multipulses,
eigenvalues,
long distance interactions,
perturbation theory for linear operators.

Mathematics Subject Classification: Primary: 47A55, 35P05; Secondary: 47A40.

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References

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