| Contents |
| We consider the introduction of $\mathcal{PT}$-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 $\mathcal{P T}$-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. |
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