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Stability domains (i.e. pump frequency detuning range) of a single dark soliton (or platicon) and dark breather in high-Q Kerr optical microresonators with normal group velocity dispersion is studied for a wide range of pump amplitudes within the framework of the Lugiato-Lefever model. The effect of the significant fragmentation of the stability domains at high pump intensities is revealed. The existence of stable drifting dark solitons (platicons) is demonstrated above the threshold pump amplitude value. Properties of drifting solitons are investigated.

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