Nonlinear Dynamics

, Volume 92, Issue 4, pp 2023–2036 | Cite as

Darboux transformation of a new generalized nonlinear Schrödinger equation: soliton solutions, breather solutions, and rogue wave solutions

  • Yaning Tang
  • Chunhua He
  • Meiling Zhou
Original Paper


In this paper, a new generalized nonlinear Schrödinger (GNLS) equation is investigated by Darboux matrix method. Firstly, the n-fold Darboux transformation (DT) of the GNLS equation is constructed. Then, the soliton solutions, breather solutions, and rogue wave solutions of the GNLS equation are studied based on the DT by choosing different seed solutions. Furthermore, the dynamic features of these solutions are explicitly delineated through some figures with the help of Maple software.


Generalized nonlinear Schrödinger equation Darboux transformation Soliton solutions Breather solutions Rogue wave solutions 



Thank our partners for their help. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Especially, we are very grateful to the editor and reviewers for their constructive comments and suggestions. This research has been supported by the Natural Science Basic Research Program of Shaanxi (No. 2017JM1024).


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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