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arXiv · 1710.05068

Universal behavior of modulationally unstable media

Gino Biondini·Sitai Li·Dionyssis Mantzavinos·Stefano Trillo
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Abstract

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.

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Gino Biondini, Sitai Li, Dionyssis Mantzavinos, Stefano Trillo. 2017-10-13. Universal behavior of modulationally unstable media. https://arxiv.org/abs/1710.05068

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