Modulational instability and nonlocality management in coupled NLS system

The modulational instability of two interacting waves in a nonlocal Kerr-type medium is considered analytically and numerically. For a generic choice of wave amplitudes, we give a complete description of stable/unstable regimes for zero group-velocity mismatch. It is shown that nonlocality suppresses considerably the growth rate and bandwidth of instability. For nonzero group-velocity mismatch we perform a geometrical analysis of a nonlocality management which can provide stability of waves otherwise unstable in a local medium.