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English

Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation

Published inPhysical Review Letters, vol. 126, no. 174501
Publication date2021
Abstract

We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, the breathing of wave packets subject to modulation instability can be stabilized as a result of the abrupt expansion a homoclinic orbit and its fall into an elliptic fixed point (center). We apply this concept to the nonlinear Schrödinger equation framework and show that an Akhmediev breather envelope, which is at the core of Fermi-Pasta-Ulam-Tsingou recurrence and extreme wave events, can be frozen into a steady periodic (dnoidal) wave by a suitable variation of a single external physical parameter. We experimentally demonstrate this general approach in the particular case of surface gravity water waves propagating in a wave flume with an abrupt bathymetry change. Our results highlight the influence of topography and waveguide properties on the lifetime of nonlinear waves and confirm the possibility to control them.

Keywords
  • Rogue waves
  • Water waves
  • Intability control
  • Surface gravity waves
  • Nonlinear waves
  • Water
  • Schrödinger equation
Funding
Citation (ISO format)
GOMEL, Alexis et al. Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation. In: Physical Review Letters, 2021, vol. 126, n° 174501. doi: 10.1103/PhysRevLett.126.174501
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Identifiers
ISSN of the journal0031-9007
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Creation04/28/2021 9:32:00 AM
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