Fundamental hydrodynamic breathers on standing waves

Physica D: Nonlinear Phenomena. 2026. Vol. 488. Article 135098.

He Y., Slunyaev A., Mori N., Kourakis I., Chabchoub A.

Extreme wave localizations in nonlinear dispersive media, arising from modulation instability in weakly nonlinear
wave interactions, can be effectively modeled by breather solutions. These breathers are exact solutions
of the nonlinear Schrödinger equation and provide accurate models for understanding and controlling unidirectional
rogue wave dynamics in numerical simulations or laboratory settings. A recent study by Y. He et al.,
Phys. Rev. Lett. 129, 144,502 (2022) offered the first proof of concept that the distinctive focusing features of
Peregrine-type breathers can persist on standing water waves, consisting of two counter-propagating wave trains
with identical carrier amplitudes and frequencies. In the present work, we report comprehensive experimental
observations of nonlinear wave focusing dynamics on standing waves using all three fundamental breather types:
the Kuznetsov-Ma, Peregrine, and Akhmediev breathers. Additionally, we extend our investigation to scenarios in
which the opposing wave field has differing amplitudes or frequencies, in order to further assess the robustness of
breather propagation under this particular cross-wave condition. The experimental results show good agreement
with the hydrodynamic coupled nonlinear Schrödinger equation (CNLSE) for the relevant cases and confirm that
both coherence and amplitude amplification of the breathers are preserved in the presence of opposing Stokes
waves. These findings further support the idea that modulation instability can prevail during the interaction of
distinct wave systems, even beyond the narrowband and unidirectional assumptions of the classical theory.

Keywords: численное моделирование, волны-убийцы, волны на воде, rogue waves, water waves, стоячие волны, Laboratory experiment, numerical simulation, лабораторный эксперимент, standing waves