On the spectrum of the superposition of separated potentials. | Zendy

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On the spectrum of the superposition of separated potentials.

Author(s) -

James Wright

Publication year - 2012

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2013.18.273

Subject(s) - spectrum (functional analysis) , superposition principle , exponential function , operator (biology) , mathematics , exponential growth , differential operator , differential equation , essential spectrum , mathematical analysis , mathematical physics , physics , pure mathematics , quantum mechanics , chemistry , biochemistry , repressor , transcription factor , gene

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.

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