Solve the coupled equations using PDE

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Hallo,Dear experts,

How to use the coefficient form of PDE equations to solve this coupled system of four equations, where the variables phiI, phiR and A need to be solved, and the V in the equation is a scalar field about phi. These equations are shown in the following picture. Additionally, this document also provides boundary conditions. My goal is to reproduce the three figures in the document. After inputting these equations and boundary conditions, I am unable to calculate the results. Is this related to the boundary conditions given in the literature? How should I solve it?

Thank you for your help!



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