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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9986114 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849414110856347648 |
|---|---|
| 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 |
| id | doaj-art-6e551201ef424dddad226dd306d4be87 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| 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 |
| work_keys_str_mv | AT dalixu equilibriumstateswithfiniteamplitudesatexactlyandnearlyclassibraggresonances AT jingyuzhang equilibriumstateswithfiniteamplitudesatexactlyandnearlyclassibraggresonances AT hongshengzhang equilibriumstateswithfiniteamplitudesatexactlyandnearlyclassibraggresonances |