Finding all roots of the system of two complex equations

I need to find all roots for the system of two complex equations. Obviously I can rewrite them as 4 real however problem remains. I have looked through routines connected with using ContourPlot however in my case they cannot be applied I think.

System is:

P1 x +I (A+a Abs[x]^2) x + I S y^2 Conjugate[x] == I F
P2 y +I (B+b Abs[y]^2) y + I S x^2 Conjugate[y] == 0

x,y are unknown variables, P1 , P2 some complex constants A,B,a,b S,F - real constants.

However problem remains, do you know an algorithm for finding all roots of 4 equations?

• Can you provide the system? – Spawn1701D Apr 17 '13 at 15:25
• Although these equations can be written with complex numbers, there is nothing inherently complex about them, as shown by the presence of constants that are real, as well as the appearance of conjugation. Inherently, then, this truly is a system of four real algebraic equations. It likely would benefit from being treated explicitly as such. – whuber Apr 17 '13 at 15:35
• Re the edit: look at Reduce, Solve, and GroebnerBasis. – whuber Apr 17 '13 at 15:59