Induced modulation instability and recurrence in nonlocal nonlinear media

The long-term behaviour of spatial modulation instability in nonlocal nonlinear Kerr media is studied theoretically and numerically. Seeding the modulation instability with a periodic modulation leads to an energy transfer to higher-order modes and the long-term behaviour of the system shows the Fermi-Pasta-Ulam recurrence. For large spatial frequencies, close to the cut-off frequency, the stable solution can be found analytically. The propagation with an initial state different from the stable solution results in a propagation circling around the stable point. For general frequencies, the calculation of the stable point is performed numerically. Comparison of the calculations with earlier reported experimental results in nematic liquid crystals shows a satisfactory agreement.