On the Spectral Stability of Kinks in Some PT‐Symmetric Variants of the Classical Klein–Gordon Field Theories. Issue 3 (18th September 2014)

• Record Type: Journal Article
• Authors: Demirkaya, A.; Kapitula, T.; Kevrekidis, P.G.; Stanislavova, M.; Stefanov, A.
• Is Part Of: Studies in applied mathematics. Volume 133:Issue 3(2014)
• Page Start: 298
• Page End: 317
• Publication Date: 2014-09-18
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/sapm.12053
• Languages: English
• ISSNs: 0022-2526

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In the present work we consider the introduction of <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1fdbqpb1" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00222526:media:sapm12053:sapm12053-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math></alternatives></inline-formula>‐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 <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1fdbqpck" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00222526:media:sapm12053:sapm12053-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math></alternatives></inline-formula>‐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.</p> </abstract>