On the stability of standing waves for 𝒫𝒯 symmetric Schrödinger and Klein-Gordon equations in higher space dimensions

Stanislavova, Milena; Stefanov, Atanas

doi:10.1090/proc/13746

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

Proc. Amer. Math. Soc. 145 (2017), 5273-5285 Request permission

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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