@John Fredsted 

thank you so much, this will be very usefull! 

@Carl Love 

Thank you so much, this is exactly what i was looking for! 

@Preben Alsholm 

I see the problem now. Sadly my tranfrormation,

is a solution of PDE. Then, i can not expand the dependense of a1(I1,E2,I2) and a3(E1,E2,I2) to a1(E1,I1,E2,I2) and a3(E1,I1,E2,I2). I've tried the diferent approach that you mensioned. And it gave me a solution that looks like yours:

If i use this solution in my tranformacion it gaves me that X1 and Y1 are equal to constants and that doesn work for me... 
I'm beginning to think that there is not a good solution to this problem...