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

Kachulin, Dmitry; Gelash, Andrey

doi:10.5194/npg-25-553-2018

Cited by 8 publications

(28 citation statements)

References 26 publications

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“…In the following two sections we present results of our study of breather collision dynamics in the framework of the Equation (1). As was noted in the Introduction, the main aim of these numerical experiments is to verify that the phase-dependent effects of breather interactions predicted recently by Kachulin and Gelash [12] can be observed in the fully nonlinear model. For this purpose, similar to the work [12], we examine overtaking collisions of breathers depending on their relative phase and wave steepness.…”

Section: Breather Collisionsmentioning

confidence: 78%

“…As was noted in the Introduction, the main aim of these numerical experiments is to verify that the phase-dependent effects of breather interactions predicted recently by Kachulin and Gelash [12] can be observed in the fully nonlinear model. For this purpose, similar to the work [12], we examine overtaking collisions of breathers depending on their relative phase and wave steepness. In addition we also study three different cases of the relative velocity between breathers.…”

Section: Breather Collisionsmentioning

confidence: 78%

“…The latter is derived using the general expression suggested by Petviashvili, applied for the particular case of the Equation (17). We refer to the monograph [27] for more general information about the Petviashvili approach, and to our previous works [12,14] for more details about its application to the Zakharov equation.…”

Section: Breather Solution Of the Zakharov Equationmentioning

confidence: 99%

“…The main aim of this work is to verify in the fully nonlinear model the effects of breather interactions predicted recently by Kachulin and Gelash [12] by using a modification of the Zakharov model-the so called super compact Dyachenko-Zakharov equation (see [13][14][15] and also [16][17][18]). The work [12] focuses on how the breather interaction dynamics depends on their relative phase. In addition to the previously known data about interactions of strongly nonlinear breathers [7], the work [12] predicts that the relative phase controls the process of energy exchange between breathers, level of energy loses and space positions of breathers after the collision.…”

Section: Introductionmentioning

confidence: 96%

“…The work [12] focuses on how the breather interaction dynamics depends on their relative phase. In addition to the previously known data about interactions of strongly nonlinear breathers [7], the work [12] predicts that the relative phase controls the process of energy exchange between breathers, level of energy loses and space positions of breathers after the collision. More precisely, the energy exchange between breathers results in increase or decrease of their amplitudes depending on the relative phase.…”

Section: Introductionmentioning

confidence: 99%

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Interactions of Coherent Structures on the Surface of Deep Water

Kachulin

Dyachenko

Gelash

2019

Fluids

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We numerically investigate pairwise collisions of solitary wave structures on the surface of deep water-breathers. These breathers are spatially localised coherent groups of surface gravity waves which propagate so that their envelopes are stable and demonstrate weak oscillations. We perform numerical simulations of breather mutual collisions by using fully nonlinear equations for the potential flow of ideal incompressible fluid with a free surface written in conformal variables. The breather collisions are inelastic. However, the breathers can still propagate as stable localised wave groups after the interaction. To generate initial conditions in the form of separate breathers we use the reduced model-the Zakharov equation. We present an explicit expression for the four-wave interaction coefficient and third order accuracy formulas to recover physical variables in the Zakharov model. The suggested procedure allows the generation of breathers of controlled phase which propagate stably in the fully nonlinear model, demonstrating only minor radiation of incoherent waves. We perform a detailed study of breather collision dynamics depending on their relative phase. In 2018 Kachulin and Gelash predicted new effects of breather interactions using the Dyachenko-Zakharov equation. Here we show that all these effects can be observed in the fully nonlinear model. Namely, we report that the relative phase controls the process of energy exchange between breathers, level of energy loses, and space positions of breathers after the collision.

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Section: Breather Collisionsmentioning

confidence: 78%

Section: Breather Collisionsmentioning

confidence: 78%

Section: Breather Solution Of the Zakharov Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Interactions of Coherent Structures on the Surface of Deep Water

Kachulin

Dyachenko

Gelash

2019

Fluids

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Investigating overtaking collisions of solitary waves in the Schamel equation

Flamarion

Pelinovsky

Didenkulova

2023

Chaos, Solitons & Fractals

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Pairwise Interactions of Coherent Structures on the Surface of Deep Water

Kachulin

Gelash

Dyachenko

et al. 2019

JOR

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The interactions of coherent structures (different types of solitary wave groups) on the surface of deep water is an important nonlinear wave process, which has been studied both theoretically and experimentally (Dyachenko et al., 2013a, b; Slunyaev et al., 2017). At the moment, a complete theoretical description of such interactions is known only for the simplest model – the nonlinear Schrödinger equation (NSE) where exact multi-soliton solutions are found. In the work (Kachulin, Gelash, 2018), the dynamics of pairwise interactions of coherent structures (breathers) on the surface of deep water were numerically investigated in the framework of the Dyachenko-Zakharov model. Significant differences were found in the collision dynamics of breathers of the compact Dyachenko-Zakharov equation when compared to the behavior of the NLSE solitons. It was found that in a more precise model of gravitational surface waves, in contrast to the NLSE, the maximum amplification of the wave field amplitude during the collision process of coherent structures can exceed the sum of the initial amplitudes of the breathers. In addition, the maximum amplification of the wave field amplitude increases with increasing steepness of the interacting breathers and exceeds unity by 20% at the value of the wave steepness m ≈ 0.2. It was revealed that an important parameter determining the dynamics of pairwise collisions of breathers is the relative phase of these objects at the moment of interaction. The interaction of breathers in the non-integrable Dyachenko-Zakharov model leads to the appearance of small radiation, which was discovered earlier in 2013 (Dyachenko et al., 2013a, b). In the work (Kachulin, Gelash, 2018) we demonstrate that the magnitude of the energy losses of the colliding solitons to radiation also depends on their relative phase. Maximum of the energy losses is observed at the same relative phase, at which the amplitude amplification maximum is observed. In addition, depending on the value of the relative phase, solitons can both gain and lose the energy, which results in increase or decrease of their amplitude after a collision. It was found that, in contrast to the NSE model, the spatial shifts of solitons in a more precise model can be both positive and negative. We use the exact breather solutions of the Dyachenko-Zakharov model and the canonical transformation to physical variables (the free surface profile and the potential on the liquid surface) to find approximate solutions in the form of breathers within the framework of exact nonlinear equations for potential incompressible fluid flows. The preliminary results of our numerical experiments in the exact model demonstrate similar dynamics of the interaction of breathers, which indicates that the theoretical picture of the interaction of coherent structures presented here is universal and can be observed in laboratory experiments. The study of the dynamics of breather interactions in the exact model performed by D.I. Kachulin was supported by the Russian Science Foundation (Grant No. 18-71-00079). The work of V.E. Zakharov and A.I. Dyachenko on the dynamics of breather interactions in approximate models was supported by the state assignment “Dynamics of the complex materials”.

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

Cited by 8 publications

References 26 publications

Interactions of Coherent Structures on the Surface of Deep Water

Interactions of Coherent Structures on the Surface of Deep Water

Investigating overtaking collisions of solitary waves in the Schamel equation

Pairwise Interactions of Coherent Structures on the Surface of Deep Water

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