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We find two types of moving dark soliton textures in elongated condensates: nonstationary kinks and proper dark solitons. The latter have a flat notch region and we obtain the diagram of their dynamical stability. At finite temperatures the dynamically stable solitons decay due to the thermodynamic instability. We develop a theory of their dissipative dynamics and explain experimental data.
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Muryshev et al. (2002) studied this question.
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