On the stability of standing waves for ${\mathcal P}{\mathcal T}$ symmetric Schrödinger and Klein-Gordon equations in higher space dimensions
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- by Milena Stanislavova and Atanas Stefanov PDF
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Abstract:
We consider ${\mathcal P}{\mathcal T}$-symmetric Schrödinger and Klein-Gordon equations in higher dimensional spaces. After the construction of the standing waves, we proceed to study their spectral stability. This extends, in the Schrödinger case, the recent results of Alexeeva et al. (2012) and Bludov et al. (2013).References
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Additional Information
- Milena Stanislavova
- Affiliation: Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, Kansas 66045–7523
- MR Author ID: 367464
- Email: stanis@ku.edu
- Atanas Stefanov
- Affiliation: Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, Kansas 66045–7523
- Email: stefanov@ku.edu
- Received by editor(s): October 3, 2016
- Received by editor(s) in revised form: December 20, 2016, and January 17, 2017
- Published electronically: July 20, 2017
- Additional Notes: The first author was supported in part by NSF-DMS # 1516245. The second author was supported in part by NSF-DMS # 1614734
- Communicated by: Catherine Sulem
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5273-5285
- MSC (2010): Primary 35B35, 35Q55, 35Q75
- DOI: https://doi.org/10.1090/proc/13746
- MathSciNet review: 3717956