Stabilization of unsteady nonlinear waves by phase space manipulation

TL;DR

This paper presents a universal method to stabilize unsteady nonlinear waves by manipulating waveguide properties, demonstrated through theoretical analysis and water wave experiments, effectively controlling wave stability and lifetime.

Contribution

The authors introduce a novel phase space manipulation technique to stabilize nonlinear waves, applicable across various physical systems, demonstrated with water wave experiments.

Findings

Wave packets can be stabilized by abrupt changes in waveguiding properties.

The method can freeze unstable wave envelopes into steady states.

Experimental validation with water waves confirms control over wave stability.

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 Schr\"odinger 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.