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 analytically and numerically. 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.
Universal behavior of modulationally unstable media
Trillo, StefanoUltimo
2018
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 analytically and numerically. 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.File | Dimensione | Formato | |
---|---|---|---|
sirev2018v60p888.pdf
solo gestori archivio
Descrizione: Full text editoriale
Tipologia:
Full text (versione editoriale)
Licenza:
NON PUBBLICO - Accesso privato/ristretto
Dimensione
7.41 MB
Formato
Adobe PDF
|
7.41 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
universal behavior of modulationally unstable media.PRE.pdf
accesso aperto
Descrizione: Pre print
Tipologia:
Pre-print
Licenza:
Creative commons
Dimensione
2.82 MB
Formato
Adobe PDF
|
2.82 MB | Adobe PDF | Visualizza/Apri |
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.