EGU General Assembly 2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation

Alexis Gomel1, Amin Chabchoub2,3,4, Maura Brunetti1, Stefano Trillo5, Jérôme Kasparian1, and Andrea Armaroli6
Alexis Gomel et al.
  • 1Institute of Environmental Science,University of Geneva, Geneva, Switzerland (
  • 2Hakubi Center for Advanced Research, Kyoto University, Kyoto, Japan
  • 3Disaster Research Institute, Kyoto University, Kyoto, Japan
  • 4School of Civil Engineering, The University of Sydney, Sydney,Australia
  • 5Deparment of Engineering, University of Ferrara, Ferrara, Italy
  • 6Institut de Recherche en Composants logiciel et matériel pour l’Information et la Communication Avancée, Université de Lille, Lille, France

We consider the stabilization of modulationally unstable wave packets by designing and abruptly changing the floor topography within the framework of the nonlinear Schrödinger equation in variable water depth [1]. This is achieved as a result of abrupt expansion of a homoclinic Akhmediev breather orbit and its into an elliptic fixed point [2,3].

We experimentally demonstrate this phenomenon process in a water wave tank and provide a rigorous theoretical description of this process. The low-dimensional theoretical predictions and measurements show that the relative phase among the side-bands locks to π and their relative amplitudes oscillates around a finite value. Apart from a 10% conversion to higher-order side-bands, this implies that the breathing stage of modulation instability (MI) is indeed frozen. This phenomenon has been also verified in an optical fiber experiment [4].

We confirm that this complex wave dynamics is robust and such control of MI processes is feasible in a realistic experimental system. Our results highlight the influence of topography and how waveguide properties can influence and manipulate the lifetime of nonlinear and extreme waves.



  • [1] Djordjevic, V. and Redekopp, L., On the development of packets of surface gravity waves moving over an uneven bottom, ZAMP 29, 950-962 (1978).
  • [2] Armaroli, A. et al., Stabilization of uni-directional water wave trains over an uneven bottom. 2021, Nonlinear Dynamics 101 , 1131-1145 (2021).
  • [3] Gomel, A. et al., Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation, Physical Review Letters 126, 174501 (2021).
  • [4] Bendahmane, A. et al., Experimental dynamics of Akhmediev breathers in a dispersion varying optical fiber, Optics Letters 39, 4490-4493 (2014).


How to cite: Gomel, A., Chabchoub, A., Brunetti, M., Trillo, S., Kasparian, J., and Armaroli, A.: Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6711,, 2022.