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.
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?