| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
|
|
|
|
Dark Localized Waves in Shallow Waters: Analysis within an Extended Boussinesq System |
| Zhengping Yang1, Wei-Ping Zhong2,3*, and Milivoj Belić3 |
1Department of Medical Science, Shunde Polytechnic, Shunde 528300, China
2Department of Electronic Engineering, Shunde Polytechnic, Shunde 528300, China
3Division of Arts and Sciences, Texas A & M University at Qatar, 23874 Doha, Qatar
|
|
| Cite this article: |
|
Zhengping Yang, Wei-Ping Zhong, and Milivoj Belić 2024 Chin. Phys. Lett. 41 044201 |
|
|
|
|
Abstract We study dark localized waves within a nonlinear system based on the Boussinesq approximation, describing the dynamics of shallow water waves. Employing symbolic calculus, we apply the Hirota bilinear method to transform an extended Boussinesq system into a bilinear form, and then use the multiple rogue wave method to obtain its dark rational solutions. Exploring the first- and second-order dark solutions, we examine the conditions under which these localized solutions exist and their spatiotemporal distributions. Through the selection of various parameters and by utilizing different visualization techniques (intensity distributions and contour plots), we explore the dynamical properties of dark solutions found: in particular, the first- and second-order dark rogue waves. We also explore the methods of their control. The findings presented here not only deepen the understanding of physical phenomena described by the (1$+$1)-dimensional Boussinesq equation, but also expand avenues for further research. Our method can be extended to other nonlinear systems, to conceivably obtain higher-order dark rogue waves.
|
|
|
Received: 04 February 2024
Published: 09 April 2024
|
|
| PACS: |
03.67.Lx
|
(Quantum computation architectures and implementations)
|
| |
03.67.-a
|
(Quantum information)
|
| |
03.65.Yz
|
(Decoherence; open systems; quantum statistical methods)
|
| |
03.67.Pp
|
(Quantum error correction and other methods for protection against decoherence)
|
|
|
|
|
|
| [1] | Akhmediev N, Dudley J M, Solli D R, and Turitsyn S K 2013 J. Opt. 15 060201 |
| [2] | Akhmediev N, Soto-Crespo J M, and Ankiewicz A 2009 Phys. Lett. A 373 2137 |
| [3] | Kharif C and Pelinovsky E 2003 Eur. J. Mech. B 22 603 |
| [4] | Walker D A G, Taylor P H, and Taylor R E 2004 Appl. Ocean Res. 26 73 |
| [5] | Draper L 1964 Oceanus 10 13 |
| [6] | Zakharov V E, Dyachenko A I, and Prokofiev A O 2006 Eur. J. Mech. B 25 677 |
| [7] | Solli D R, Ropers C, and Koonath P 2007 Nature 450 1054 |
| [8] | Akhmediev N, Kibler B, Baronio F et al. 2016 J. Opt. 18 063001 |
| [9] | Zhong W P, Belić M R, and Huang T 2013 Phys. Rev. E 87 065201 |
| [10] | Akhmediev N, Ankiewicz A, and Soto-Crespo J M 2009 Phys. Rev. E 80 026601 |
| [11] | Zhong W P, Chen L, Belić M, and Petrović N 2014 Phys. Rev. E 90 043201 |
| [12] | Kedziora D J, Ankiewicz A, and Akhmediev N 2013 Phys. Rev. E 88 013207 |
| [13] | Yang J and Zhu Y 2023 Phys. Lett. A 487 129117 |
| [14] | Zhong W P, Belić M, and Malomed B A 2015 Phys. Rev. E 92 053201 |
| [15] | Sun W R and Liu M M 2022 Phys. Lett. A 456 128539 |
| [16] | Yang Z P, Zhong W P, Belić M, and Zhang Y Q 2018 Opt. Express 26 7587 |
| [17] | Xu S Y, Zhou Q, and Liu W 2023 Nonlinear Dyn. 111 18401 |
| [18] | Liu X M, Zhang Z Y, and Liu W J 2023 Chin. Phys. Lett. 40 070501 |
| [19] | Wen X K, Jiang J H, Liu W, and Dai C Q 2023 Nonlinear Dyn. 111 13343 |
| [20] | Wang S B, Ma G L, Zhang X, and Zhu D Y 2022 Chin. Phys. Lett. 39 114202 |
| [21] | Boussinesq J 1871 Comptes Rendus de l' Academie des Sciences 72 755 |
| [22] | Zhu J Y 2017 arXiv:1704.02779 [nlin.SI] |
| [23] | Cao Y L, He J S, and Mihalache D 2018 Nonlinear Dyn. 91 2593 |
| [24] | Ma W X, Li C X, and He J 2009 Nonlinear Anal. 70 4245 |
| [25] | Wazwaz A M 2008 Appl. Math. Comput. 203 277 |
| [26] | Hirota R 1973 J. Math. Phys. 14 805 |
| [27] | Zhong W P, Belić M, Assanto G, Malomed B A, and Huang T 2011 Phys. Rev. A 84 043801 |
| [28] | Clarkson P A and Dowie E 2017 Trans. Math. Its Appl. 1 tnx003 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
