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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/npg-2018-14
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
05 Mar 2018
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).
Phase-dependent dynamics of breather collisions in the compact Zakharov equation for envelope
Dmitry Kachulin1 and Andrey Gelash1,2 1Novosibirsk State University, Novosibirsk, 630090, Russia
2Institute of Thermophysics, SB RAS, Novosibirsk, 630090, Russia
Abstract. We study collisions of the solitary type coherent wave structures – breathers in the nonintegrable Zakharov equation for envelope describing gravity waves on the surface of deep water. The numerical simulations of breather interactions revealed several fundamentally different effects when compared to analytical two-soliton solutions of the nonlinear Schrodinger equation. The relative phase of the breathers is shown to be the key parameter determining the dynamics of the interaction. We show that the maximum of the amplitude amplification can significantly exceed the sum of the breather amplitudes. The breathers lose up to a few percent of their energy during the collisions due to radiation of incoherent waves and in addition exchange energy with each other. The level of the energy loss increases with large values of the wave steepness, and also with certain synchronisation of breather phases. Each of the breathers can gain or lose the energy after collision resulting in the increase or decrease of the amplitude. The magnitude of the space shifts that breathers acquire after collisions depends on the relative phase and can be either positive or negative.
Citation: Kachulin, D. and Gelash, A.: Phase-dependent dynamics of breather collisions in the compact Zakharov equation for envelope, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2018-14, in review, 2018.
Dmitry Kachulin and Andrey Gelash
Dmitry Kachulin and Andrey Gelash
Dmitry Kachulin and Andrey Gelash

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Short summary
We consider the well known in geophysics nonlinear model for deep water surface gravity waves – the envelope Zakharov equation. This model predicts that waves can propagate as a stable localized groups – breathers. We study numerically in details the breather collision process and found several fundamentally different effects when compared to the previously known results. In particular we show the formation of extreme amplitude waves, that may cause serious damage when appear in seas and oceans.
We consider the well known in geophysics nonlinear model for deep water surface gravity waves –...
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