Is it possible to solve nonlinear PDE with complex dependent variable using FDM?

Hello, I'm working to solve a nonlinear PDE with complex numbers term and the dependent variable is also complex,the two independent variables are real and the other dependent(H_0&P_0) also are real, (Q_E10) is complex variable ,(H_0&P_0) are known as two matrix for a mesh region...any help please.