Question: solving a PDE system with constant parameters

Hi guys! 

I have a PDE system. The mayority of the equations are equal to zero, but two of them are:


where a, b, c, d are CONSTANT parameters. I know that if a=b=d=c=1 the system is inconsistent. But I also know that if a=-1, b=d=0 and c=1 the system is consistent and exist the solution. I wanna know if there's a way to ask maple to find another selections of my parameter that make my PDE consistent and what it's the solution for that selection of a,b,c,d. 

Here's my PDE system (sys2).

thank you so much for your time! 

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