Abstract
Higher-order rogue wave solutions have vital applications in nonlinear physics. The new modified Gerdjikov–Ivanov equation with dispersion is derived for the first time in this paper. Based on the extend Lax pair, the localized waves of the new model are obtained via generalized Darboux transformation, the higher-order rogue solutions are presented graphically and their dynamic properties are analyzed. The results obtained have spurred the study of higher-order dispersion equations in nonlinear optics.
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