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On the stability of standing waves for $ {\mathcal P}{\mathcal T}$ symmetric Schrödinger and Klein-Gordon equations in higher space dimensions


Authors: Milena Stanislavova and Atanas Stefanov
Journal: Proc. Amer. Math. Soc. 145 (2017), 5273-5285
MSC (2010): Primary 35B35, 35Q55, 35Q75
DOI: https://doi.org/10.1090/proc/13746
Published electronically: July 20, 2017
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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).


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Additional Information

Milena Stanislavova
Affiliation: Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, Kansas 66045–7523
Email: stanis@ku.edu

Atanas Stefanov
Affiliation: Department of Mathematics, University of Kansas, 1460 Jayhawk Boulevard, Lawrence, Kansas 66045–7523
Email: stefanov@ku.edu

DOI: https://doi.org/10.1090/proc/13746
Keywords: ${\mathcal P}{\mathcal T}$ symmetry, Schr\"odinger equation, wave equation
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
Article copyright: © Copyright 2017 American Mathematical Society