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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 25, issue 3 | Copyright
Nonlin. Processes Geophys., 25, 553-563, 2018
https://doi.org/10.5194/npg-25-553-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 15 Aug 2018

Research article | 15 Aug 2018

On the phase dependence of the soliton collisions in the Dyachenko–Zakharov envelope equation

Dmitry Kachulin1 and Andrey Gelash1,2 Dmitry Kachulin and Andrey Gelash
  • 1Novosibirsk State University, Novosibirsk, 630090, Russia
  • 2Institute of Thermophysics, SB RAS, Novosibirsk, 630090, Russia

Abstract. We study soliton collisions in the Dyachenko–Zakharov equation for the envelope of gravity waves in deep water. The numerical simulations of the soliton interactions revealed several fundamentally different effects when compared to analytical two-soliton solutions of the nonlinear Schrodinger equation. The relative phase of the solitons is shown to be the key parameter determining the dynamics of the interaction. We find that the maximum of the wave field can significantly exceed the sum of the soliton amplitudes. The solitons 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 certain synchronization of soliton phases. Each of the solitons can gain or lose the energy after collision, resulting in increase or decrease in the amplitude. The magnitude of the space shifts that solitons acquire after collisions depends on the relative phase and can be either positive or negative.

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We consider the nonlinear model well known in geophysics for deep water surface gravity waves – the envelope version of the Dyachenko–Zakharov equation. This model predicts that waves can propagate as a stable localized groups – solitons. We study numerically in detail the soliton collisions and find fundamentally different effects when compared to the previously known results. We demonstrate the formation of extreme amplitude waves that may cause serious damage appearing in seas and oceans.
We consider the nonlinear model well known in geophysics for deep water surface gravity waves –...
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