On Nth-order rogue wave solution to the generalized nonlinear Schrödinger equation |
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| Authors: | Zhaqilao |
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| Institution: | 1. College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022, China;2. Department of Mathematics Science, Tsinghua University, Beijing 100084, China |
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| Abstract: | In this Letter, the generalized nonlinear Schrödinger (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. |
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| Keywords: | Rogue wave solution Generalized nonlinear Schrö dinger equation Generalized Darboux transformation |
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