Hey everyone,

f_1 and f_2 are satisfying the set of non-linear integral equations I have attached to this message.

I know that I need to solve them numerically by iterations. Probably, the first guest of the function f_1 and f_2 is the driving term. a is just a parameter which can be fixed (I guess smaller than \pi/4). * is the convolution product and k is the momentum space parameter. I learnt that in order to solve them I should solve them in the Fourier space. I know also that I need to discretize these function in the “real ” space between {-L,+L} before applying the FFT or one of its relatives. Thank you for any suggestions or leads.