Abstract
In this paper, we investigate the dynamics of localized waves for the higher-order modified Gerdjikov–Ivanov equation. Based on Lax pair, the Nth-fold Darboux transformation is constructed. The soliton, breather and rogue wave solutions are obtained and presented graphically. Moreover, the dynamic properties of the above localized waves are analyzed. Specially, the interactions between solitons and bound states are achieved. In addition, the rational W-shaped soliton is derived by the degeneration of breather solutions.
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