Conserved Gross-Pitaevskii equations with a parabolic potential  

作　　者：Shi-min Liu Da-jun Zhang 

机构地区：[1]Department of Mathematics,Shanghai University,Shanghai 200444,People’s Republic of China

出　　处：《Communications in Theoretical Physics》2022年第10期30-36,共7页理论物理通讯（英文版）

基　　金：supported by the NSF of China (Nos. 11 875 040, 12 126 352, 12 126 343)。

摘　　要：An integrable Gross–Pitaevskii equation with a parabolic potential is presented where particle density|u|^(2)is conserved.We also present an integrable vector Gross–Pitaevskii system with a parabolic potential,where the total particle density∑^(n)_(j)=_(1)∣u_(j)∣^(2)is conserved.These equations are related to nonisospectral scalar and vector nonlinear Schrödinger equations.Infinitely many conservation laws are obtained.Gauge transformations between the standard isospectral nonlinear Schrödinger equations and the conserved Gross–Pitaevskii equations,both scalar and vector cases are derived.Solutions and dynamics are analyzed and illustrated.Some solutions exhibit features of localized-like waves.

关 键 词：Gross-Pitaevskii equation gauge transformation nonisospectral conserved particle density 

分 类 号：O302[理学—力学]