Perturbation methods are used to study the dynamics of locked fluxon modes on stacked Josephson junctions and single crystals of certain high-Tc superconductors. Two limiting cases are considered: (i) The non- linear diffusion regime in which fluxon dynamics are dominated by energy exchange between the bias and loss parameters, and (ii) The propagating regime in which the interplay between magnetic and electric field energies governs the fluxon dynamics. Conditions for stability of locked fluxon modes are shown to be different in these two regimes.
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