A (3+1)-dimensional variable-coefficient partially nonlocal coupled Gross–Pitaevskii equation trapped in a harmonic potential becomes a focus of this paper. A counterpart of this variable-coefficient coupled equation is found as a (2+1)-dimensional constant-coefficient single nonlinear Schrödinger equation via the reduction procedure. By solutions of constant-coefficient single equation via the Hirota method, and from this counterpart, analytical high-dimensional vector soliton solutions with the Hermite–Gaussian envelope of the variable-coefficient coupled equation are deduced. Expanded behaviors of high-dimensional vector solitons emerge in the exponential diffraction decreasing system.

一个（3+1）维可变系数部分非局部耦合的 Gross-Pitaevskii 方程被困在谐波势中成为本文的重点。这个可变系数耦合方程的对应物被发现为 (2+1) 维常数系数单一非线性薛定谔方程，通过归约过程。通过Hirota方法对恒系数单方程的解，并由此推导出具有变系数耦合方程的Hermite-Gaussian包络的解析高维矢量孤子解。指数衍射递减系统中出现了高维矢量孤子的扩展行为。