Abstract

Abstract In this Letter, the generalized nonlinear Schrodinger (GNLS) equation is investigated by Darboux matrix method. A generalized Darboux transformation (DT) of the GNLS equation is constructed with the help of the gauge transformation for an Ablowitz–Kaup–Newell–Segur (AKNS) type GNLS spectral problem, from which a unified formula of N th-order rogue wave solution to the GNLS equation is given. In particular, the first and second-order rogue wave solutions to the GNLS equation are explicitly illustrated through some figures.

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