Quantised vortices, travelling coherent structures and superfluid turbulence

The Gross-Pitaevskii equation and its modifications are used to elucidate different aspects of superfluid behaviour: motion of vortices, travelling waves, interactions with normal fluid and superfluid turbulence. Different mechanisms of formation of travelling coherent structures are considered. They are formed when a critical velocity is exceeded in the flow. They can appear as a result of instabilities or energy transfer among waves. They are formed together with the formation of condensate, but the interactions with normal fluid (non-condensed particles) lead to their dissipation.