The vector soliton of the (3+1)-dimensional Gross-Pitaevskii equation with variable coefficients

In this paper, a variable coefficient (3+1)-dimensional Gross-Pitaevskii equation is used to study the propagation properties of solitons in Bose-Einstein condensation, as well as the influence of nonlinear terms of time modulation on the properties of solitons. Under reasonable assumptions, the 1-, 2-, 3-soliton solutions of Gross-Pitaevskii equation are constructed by Hirota bilinear method. The results indicate that they can be transformed into special soliton solutions (bright, dark and periodic) under certain conditions. On this basis, the figures of various soliton solutions are displayed, and the influence of coefficient function on soliton solutions is discussed. It is found that the influence of variable coefficients on the physical quantities of several types of soliton solutions has different emphases, and specific laws of influence are derived. In addition, in order to better understand the dynamic properties of soliton solutions, the asymptotic behavior of 2-, 3-soliton solutions is analyzed. Our research can provide a theoretical basis for the dynamics problem in Bose-Einstein condensation.