Spectral stability analysis for standing waves of a perturbed\n Klein-Gordon equation

2014/09/24 by Aslihan Demirkaya, Demirkaya, Aslihan, P. G. Kevrekidis +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Quantum Mechanics and Non-Hermitian Physics #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.1409.7095

Abstract

In the present work, we introduce a new \PT-symmetric variant of\nthe Klein-Gordon field theoretic problem. We identify the standing wave\nsolutions of the proposed class of equations and analyze their stability. In\nparticular, we obtain an explicit frequency condition, somewhat reminiscent of\nthe classical Vakhitov-Kolokolov criterion, which sharply separates the regimes\nof spectral stability and instability. Our numerical computations corroborate\nthe relevant theoretical result.\n

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