  Evidence is presented of universal behavior in modulationally unstable media.
An ensemble of nonlinear evolution equations, including three partial
differential equations, an integro-differential equation, a nonlocal system and
a differential-difference equation, is studied. Collectively, these systems
arise in a variety of applications in the physical and mathematical sciences,
including water waves, optics, acoustics, Bose-Einstein condensation, and more.
All these models exhibit modulational instability, namely, the property that a
constant background is unstable to long-wavelength perturbations. In this work,
each of these systems is studied analytically and numerically for a number of
different initial perturbations of the constant background, and it is shown
that, for all systems and for all initial conditions considered, the dynamics
gives rise to a remarkably similar structure comprised of two outer, quiescent
sectors separated by a wedge-shaped central region characterized by modulated
periodic oscillations. A heuristic criterion that allows one to compute some of
the properties of the central oscillation region is also given.
