Abstract
The nonlinear collective dynamics of a one-dimensional cold atomic cloud is investigated using a Lagrangian fluid description. An exact non-stationary nonlinear solution with a nontrivial space and time dependence is obtained. The results demonstrate the formation of nonlinear localized soliton-like density structures when nonlinearity is being balanced by the wave dispersion. Moreover, the solution predicts the catastrophic density collapse in the cloud of cold atomic gas when nonlinearity overpowers the dispersion.
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