# American Institute of Mathematical Sciences

July  2018, 17(4): 1371-1385. doi: 10.3934/cpaa.2018067

## 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

Received  January 2017 Revised  June 2017 Published  April 2018

Fund Project: 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.

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.

Citation: Wen Feng, Milena Stanislavova, Atanas Stefanov. On the spectral stability of ground states of semi-linear Schrödinger and Klein-Gordon equations with fractional dispersion. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1371-1385. doi: 10.3934/cpaa.2018067
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