Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation.

Area of Science:

• Nonlinear physics
• Wave dynamics
• Fluid mechanics

Background:

• Nonlinear coherent waves, such as Akhmediev breathers, are fundamental to understanding phenomena like Fermi-Pasta-Ulam-Tsingou recurrence and extreme wave events.
• Modulation instability often leads to the 'breathing' or unpredictable evolution of wave packets.
• Controlling the dynamics and lifetime of these nonlinear waves remains a significant challenge.

Purpose of the Study:

• To introduce a universally applicable dynamic stabilization scheme for unidirectional nonlinear coherent waves.
• To demonstrate the stabilization of wave packets subject to modulation instability.
• To experimentally validate this stabilization approach in surface gravity water waves.

Main Methods:

• Implementing a dynamic stabilization scheme by abruptly changing waveguiding properties.
• Applying the nonlinear Schrödinger equation framework to model wave packet behavior.
• Utilizing an abrupt bathymetry change in a wave flume for experimental demonstration.

Main Results:

• Stabilization of wave packets by transitioning from a homoclinic orbit to an elliptic fixed point.
• Freezing of Akhmediev breather envelopes into steady periodic (dnoidal) waves via parameter variation.
• Experimental confirmation of wave control through changes in topography and waveguide properties.

Conclusions:

• The proposed dynamic stabilization scheme is universally applicable to nonlinear coherent waves.
• Topography and waveguide properties significantly influence the lifetime of nonlinear waves.
• It is possible to control and stabilize extreme wave events using this method.