Abstract
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.
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