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On the stability analysis of periodic sine-Gordon traveling waves
We study the spectral stability properties of periodic traveling waves in the
sine-Gordon equation, including waves of both subluminal and superluminal
propagation velocities as well as waves of both librational and rotational
types. We prove that only subluminal rotational waves are spectrally stable and
establish exponential instability in the other three cases. Our proof corrects
a frequently cited one given by Scott.Comment: 22 pages, 6 figure
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