We present results of a numerical and analytical study of the dc-driven, damped sine-Gordon equation with periodic boundary conditions. We find that this system is characterized by competitions between two classes of multisoliton--wave-train, space-time structures; phase-locked (cavity-mode) states and kink-antikink (fluxon-antifluxon) pairs. We also find that a variety of pattern transitions occur between these states. Our results are reported in the language of zero-field steps in annular Josephson junctions and transverse instabilities on propagating interfaces in, e.g., charge-density-wave materials and crystals.
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Ariyasu et al. (1987) studied this question.
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