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.
基金项目
国家自然科学基金(62275176)
广东省自然科学基金(2022A1515010084)
Key projects of basic research and applied basic research in universities of Guangdong province,China(2021ZDZX1118)
Key projects of basic research and applied basic research in universities of Guangdong province,China(2022ZDZX1079)
Qatar National Research Fund(a member of Qatar Foundation)(NPRP 13S-0121-200126)
维普
万方数据