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Solutions and connections of nonlocal derivative nonlinear Schrödinger equations

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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.

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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).

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Authors and Affiliations

  1. School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023, Zhejiang Province, People’s Republic of China

    Ying Shi

  2. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, Zhejiang Province, People’s Republic of China

    Shou-Feng Shen & Song-Lin Zhao

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  1. Ying Shi
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  2. Shou-Feng Shen
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Correspondence to Ying Shi.

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Shi, Y., Shen, SF. & Zhao, SL. Solutions and connections of nonlocal derivative nonlinear Schrödinger equations. Nonlinear Dyn 95, 1257–1267 (2019). https://doi.org/10.1007/s11071-018-4627-x

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