In this article, a (3+1)-dimensional variable coefficients coupled nonlinear Schrö-dinger equation is analysed with the unified method, the improved F-expansion method with Riccati equation and the modified Kudryashov method. The polynomial solutions are investigated and classified into three categories including complex solitary wave solutions, complex soliton wave solutions and complex elliptic wave solutions by applying the unified method. Besides, the physical insights of polynomial solutions are graphically discussed with suitable parameters. The complex wave solutions are derived by the improved F-expansion method with Riccati equation which contain the complex hyperbolic trigonometric solutions, complex trigonometric solutions and complex rational solutions. Lastly, the modified Kudryashov method is applied to obtain the complex wave solutions.

本文将（3 + 1）维变系数耦合非线性Schr$\ddot{\mathrm{Ø}}$统一方法分析了dinger方程，改进了Riccati方程的F展开法和改进的Kudryashov方法。应用统一方法对多项式解进行了研究，并将其分为复杂的孤立波解，复杂的孤子波解决方案和复杂的椭圆波解三类。此外，还使用适当的参数以图形方式讨论了多项式解的物理见解。复波解是通过改进的F展开方法和Riccati方程得出的，其中包括复双曲三角解，复三角解和复有理解。最后，采用改进的Kudryashov方法获得了复波解。