Solving the Balitsky-Kovchegov equation at next to leading order accuracy

We solve the Balitsky-Kovchegov small-x evolution equation in coordinate space. We find that the solution to the equation is unstable when using an initial condition relevant for phenomenological applications at leading order. The problematic behavior is shown to be due to a large double logarithmic contribution. The same problem is found when the evolution of the “conformal dipole” is solved, even though the double logarithmic term is then absent from the evolution equation.