Equilibrium States with Finite Amplitudes at Exactly and Nearly Class-I Bragg Resonances

The exactly and nearly class-I Bragg resonances of strongly nonlinear waves are studied analytically by the homotopy analysis method. Two types of equilibrium states with time-independent wave spectra and different energy distributions are obtained. Effects of the incident wave height, the seabed he...

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Main Authors: Dali Xu, Jingyu Zhang, Hongsheng Zhang
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/9986114
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author Dali Xu
Jingyu Zhang
Hongsheng Zhang
author_facet Dali Xu
Jingyu Zhang
Hongsheng Zhang
author_sort Dali Xu
collection DOAJ
description The exactly and nearly class-I Bragg resonances of strongly nonlinear waves are studied analytically by the homotopy analysis method. Two types of equilibrium states with time-independent wave spectra and different energy distributions are obtained. Effects of the incident wave height, the seabed height, and the frequency detuning on resonant waves are investigated. Bifurcation points of the equilibrium states are found and tend to greater value of relatively incident wave height for a steeper wave. The wave steepness of the whole wave system grows linearly with the seabed height. Meanwhile, the resonant peak can shift to up or down side when the near resonance is considered. This work provides us a deeper understanding on class-I Bragg resonance and enlightens further studies of higher-order wave-bottom interactions.
format Article
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institution Kabale University
issn 2314-4629
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language English
publishDate 2021-01-01
publisher Wiley
record_format Article
series Journal of Mathematics
spelling doaj-art-6e551201ef424dddad226dd306d4be872025-08-20T03:33:56ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/99861149986114Equilibrium States with Finite Amplitudes at Exactly and Nearly Class-I Bragg ResonancesDali Xu0Jingyu Zhang1Hongsheng Zhang2College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, ChinaCollege of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, ChinaCollege of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, ChinaThe exactly and nearly class-I Bragg resonances of strongly nonlinear waves are studied analytically by the homotopy analysis method. Two types of equilibrium states with time-independent wave spectra and different energy distributions are obtained. Effects of the incident wave height, the seabed height, and the frequency detuning on resonant waves are investigated. Bifurcation points of the equilibrium states are found and tend to greater value of relatively incident wave height for a steeper wave. The wave steepness of the whole wave system grows linearly with the seabed height. Meanwhile, the resonant peak can shift to up or down side when the near resonance is considered. This work provides us a deeper understanding on class-I Bragg resonance and enlightens further studies of higher-order wave-bottom interactions.http://dx.doi.org/10.1155/2021/9986114
spellingShingle Dali Xu
Jingyu Zhang
Hongsheng Zhang
Equilibrium States with Finite Amplitudes at Exactly and Nearly Class-I Bragg Resonances
Journal of Mathematics
title Equilibrium States with Finite Amplitudes at Exactly and Nearly Class-I Bragg Resonances
title_full Equilibrium States with Finite Amplitudes at Exactly and Nearly Class-I Bragg Resonances
title_fullStr Equilibrium States with Finite Amplitudes at Exactly and Nearly Class-I Bragg Resonances
title_full_unstemmed Equilibrium States with Finite Amplitudes at Exactly and Nearly Class-I Bragg Resonances
title_short Equilibrium States with Finite Amplitudes at Exactly and Nearly Class-I Bragg Resonances
title_sort equilibrium states with finite amplitudes at exactly and nearly class i bragg resonances
url http://dx.doi.org/10.1155/2021/9986114
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AT jingyuzhang equilibriumstateswithfiniteamplitudesatexactlyandnearlyclassibraggresonances
AT hongshengzhang equilibriumstateswithfiniteamplitudesatexactlyandnearlyclassibraggresonances