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On the Spectral Stability of Kinks in Some PT ‐Symmetric Variants of the Classical Klein–Gordon Field Theories
Author(s) -
Demirkaya A.,
Kapitula T.,
Kevrekidis P.G.,
Stanislavova M.,
Stefanov A.
Publication year - 2014
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12053
Subject(s) - linearization , context (archaeology) , klein–gordon equation , spectrum (functional analysis) , field (mathematics) , physics , mathematical physics , stability (learning theory) , lossy compression , classical mechanics , mathematics , mathematical analysis , nonlinear system , quantum mechanics , pure mathematics , paleontology , statistics , machine learning , computer science , biology
In the present work we consider the introduction of PT ‐symmetric terms in the context of classical Klein–Gordon field theories. We explore the implication of such terms on the spectral stability of coherent structures, namely kinks. We find that the conclusion critically depends on the location of the kink center relative to the center of the PT ‐symmetric term. The main result is that if these two points coincide, the kink's spectrum remains on the imaginary axis and the wave is spectrally stable. If the kink is centered on the “lossy side” of the medium, then it becomes stabilized. On the other hand, if it becomes centered on the “gain side” of the medium, then it is destabilized. The consequences of these two possibilities on the linearization (point and essential) spectrum are discussed in some detail.