On the spectral stability of ground states of semi-linear Schrödinger and Klein-Gordon equations with fractional dispersion

Wen Feng; Milena Stanislavova; Atanas Stefanov

doi:10.3934/cpaa.2018067

Article Contents

2018, Volume 17, Issue 4: 1371-1385. Doi: 10.3934/cpaa.2018067

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On the spectral stability of ground states of semi-linear Schrödinger and Klein-Gordon equations with fractional dispersion

Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, KS 66045, USA

^* Corresponding author
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Received: January 2017

Revised: June 2017

Published: April 2018

Feng is supported by a graduate fellowship under grant # 1516245. Stanislavova is partially supported by NSF-DMS, Applied Mathematics program, under grant # 1516245. Stefanov is supported by NSF-DMS, Applied Mathematics program, under grant # 1614734.

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Abstract

We consider standing wave solutions of various dispersive models with non-standard form of the dispersion terms. Using index count calculations, together with the information from a variational construction, we develop sharp conditions for spectral stability of these waves.

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Mathematics Subject Classification: Primary: 35B35, 35B40; Secondary: 35G30.

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