Abstract
Via Darboux transformation (DT) algorithm, rogue wave and semi-rational solutions of the mixed nonlinear Schrödinger equation (MNLSE) will be derived. Meanwhile, the dynamic features of those solutions will be graphically analyzed. In addition, the modulation instability (MI) of the MNLSE will be discussed and it will be found that the existence range of rogue waves is strictly consistent with the zero frequency modulation instability region.
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