A Lagrangian approach to modulational instability in nonlocal nonlinear Kerr media

Using a time-dependent variational approach to study modulational instability (MI) of plane waves in Kerr media with nonlocal nonlinearity in its linear stage, I obtain and analyze the set of ordinary differential equations that describe the evolution over time of the amplitude and phase of modulational perturbations. From those equations, I obtain the effective potential of the system and perform numerical simulations to verify the theoretical results. For the nonlinear stage, I find that the degree of nonlocality notably changes the behavior of MI in the central oscillatory region of the integration.