New dynamics of the classical and nonlocal Gross-Pitaevskii equation with a parabolic potential

Shi-min Liu, Hua Wu, Da-jun Zhang

备注：: 21 pages, 7 figures
DOI：: 10.1016/S0034-4877(20)30083-5

英文摘要：

Solutions of the classical and nonlocal Gross-Pitaevskii (GP) equation with a parabolic potential and a gain term are derived by using a second order nonisospectral Ablowitz-Kaup-Newell-Segur system and reduction technique of double Wronskians. Solutions of the classical GP equation show typical space-time localized characteristics. An interesting dynamics, solitons carrying an oscillating wave, are found with mathematical analysis and illustrations. Solutions of some nonlocal cases are also illustrated.

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