Abstract
The Hirota bilinear method is studied in a lot of local equations, but there are few work to solve nonlocal equations with external potential by Hirota bilinear method. In this letter, we succeed to bilinearize the generalized nonlocal Gross–Pitaevskii (NGP) equation with an arbitrary time-dependent linear potential through a nonstandard procedure and present more general bright soliton solutions, which describes the dynamics of soliton solutions in quasi-one-dimensional Bose–Einstein condensations. Under some reasonable assumptions, one-bright-soliton and two-bright-soliton solutions are constructed analytically by the improved Hirota method. From the gauge equivalence, we can see the difference between the solutions of the nonlocal GP equation and the solutions of the local GP equation.
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