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.

Phys. Rev. Lett.

Muryshev, A. E, Shlyapnikov, G. V, Ertmer, W, Sengstock, K, & Lewenstein, M. (2002). Dynamics of dark solitons in elongated Bose-Einstein condensates. Phys.Rev.Lett., 89(Article number: 110401), 1–4.