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Solutions and connections of nonlocal derivative nonlinear Schrödinger equations

  • Ying Shi
  • Shou-Feng Shen
  • Song-Lin Zhao
Original Paper
  • 20 Downloads

Abstract

All possible nonlocal versions of the derivative nonlinear Schrödinger equations are derived by the nonlocal reduction from the Chen–Lee–Liu equation, the Kaup–Newell equation and the Gerdjikov–Ivanov equation which are gauge equivalent to each other. Their solutions are obtained by composing constraint conditions on the double Wronskian solution of the Chen–Lee–Liu equation and the nonlocal analogues of the gauge transformations among them. Through the Jordan decomposition theorem, those solutions of the reduced equations from the Chen–Lee–Liu equation can be written as canonical form within real field.

Keywords

Nonlocal derivative nonlinear Schrödinger equations Nonlocal reduction Double Wronskian Canonical form 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (NSFC) grant (Grant Number 11501510) and the Natural Science Foundation of Zhejiang Province (No. LY17A010024).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of ScienceZhejiang University of Science and TechnologyHangzhouPeople’s Republic of China
  2. 2.Department of Applied MathematicsZhejiang University of TechnologyHangzhouPeople’s Republic of China

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