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Modulation instability, higher-order rogue waves and dynamics of the Gerdjikov–Ivanov equation
Wave Motion ( IF 2.4 ) Pub Date : 2021-07-03 , DOI: 10.1016/j.wavemoti.2021.102795
Yu Lou 1 , Yi Zhang 1 , Rusuo Ye 1 , Miao Li 1
Affiliation  

We investigate the modulation instability and higher-order rogue waves for the Gerdjikov–Ivanov equation. Based on the theory of the linear stability analysis, the modulation instability is the condition of the existence of the rogue waves. With the help of Darboux transformation and a variable separation technique, the formula of the higher-order rogue wave solutions is given explicitly. The kinetics of the first-, second-, and third-order rogue wave solutions are elucidated from the viewpoint of three-dimensional structures. More specifically, it is shown that this method is fairly powerful and handy to obtain the higher-order rogue wave solutions which appear in different phenomena in applied sciences and mathematical physics.



中文翻译:

Gerdjikov-Ivanov 方程的调制不稳定性、高阶流氓波和动力学

我们研究了 Gerdjikov-Ivanov 方程的调制不稳定性和高阶流氓波。根据线性稳定性分析理论,调制不稳定性是杂波存在的条件。借助 Darboux 变换和变量分离技术,明确给出了高阶流氓波解的公式。从三维结构的角度阐明了一阶、二阶和三阶流氓波解的动力学。更具体地说,它表明这种方法在获得应用科学和数学物理中不同现象中出现的高阶流氓波解方面是相当强大和方便的。

更新日期:2021-07-07
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