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

• * Corresponding author
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.

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

 Citation:

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