TY - JOUR
T1 - Dark Localized Waves in Shallow Waters
T2 - Analysis within an Extended Boussinesq System
AU - Yang, Zhengping
AU - Zhong, Wei Ping
AU - Belić, Milivoj
N1 - Publisher Copyright:
© 2024 Chinese Physical Society and IOP Publishing Ltd.
PY - 2024/4/1
Y1 - 2024/4/1
N2 - 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.
AB - 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.
KW - Soliton solutions
UR - http://www.scopus.com/inward/record.url?scp=85190578794&partnerID=8YFLogxK
U2 - 10.1088/0256-307X/41/4/044201
DO - 10.1088/0256-307X/41/4/044201
M3 - Article
AN - SCOPUS:85190578794
SN - 0256-307X
VL - 41
JO - Chinese Physics Letters
JF - Chinese Physics Letters
IS - 4
M1 - 044201
ER -