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.

在许多局部方程中研究了Hirota双线性方法，但是通过Hirota双线性方法来求解具有外部势的非局部方程的工作很少。在这封信中，我们通过非标准程序成功地将具有任意随时间变化的线性势的广义非局部Gross-Pitaevskii（NGP）方程双线性化，并给出了更通用的明亮孤子解，它描述了准一维孤子解的动力学。三维玻色–爱因斯坦凝聚。在一些合理的假设下，通过改进的Hirota方法解析地构造了一亮孤子和二亮孤子解。从规范的等价关系中，我们可以看到非局部GP方程的解与局部GP方程的解之间的差异。