On Nth-order rogue wave solution to the generalized nonlinear Schrodinger equation

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 Nth-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. (c) 2013 Elsevier B.V. All rights reserved.