Abstract
It is shown that Gross–Pitaevskii equation with parabolic potential has solutions in form of localized wave packets, which are self-similar and undergo periodic spatial oscillations. The proposed solutions combine some properties of coherent states of quantum optics and solitons of the nonlinear Schrödinger equation, and are expressed in terms of spatially shifted and phase-modulated solutions of nonlinear second order ordinary differential equation.
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