discrete equation which has initial value with periodic boundary condition(please help)

hello i have a equation

i (dc/dt) = -(cn+1 +cn-1)+ lcnl^2 cn (n subtitle) if i divide it into 200 part c201=c1

initial value is something like that c(x,0)=1-(4/ 1+x^2);

i tried to solve this problem with cranck-nicolson method but it failed. Is there something different method or special numerically solver technique? Thanks for your help...