PAINLEVÉ ANALYSIS, LAX PAIR AND BÄCKLUND TRANSFORMATION FOR THE GROSS–PITAEVSKII EQUATION IN THE BOSE–EINSTEIN CONDENSATES

Due to their relevance to physics and technology, the Bose–Einstein condensates (BECs) are of current interest. Certain dynamics of the BECs, such as the cigar-shaped condensate confined in a cylindrically symmetric parabolic trap, can be described by the Gross–Pitaevskii (GP) equation with a time-dependent trap. In this paper, by virtue of the Painlevé analysis and symbolic computation, we derive the integrable condition for the GP equation …