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

2015 11 3
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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.

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