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A novel reduction approach to obtain \({\varvec{N}}\)-soliton solutions of a nonlocal nonlinear Schrödinger equation of reverse-time type

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Abstract

In this paper, a novel reduction approach is reported for a physically meaningful nonlocal nonlinear Schrödinger (NLS) equation of reverse-time type to obtain its N-soliton solutions. Firstly, single-soliton solutions of the nonlocal NLS equation are obtained by reducing those of the local NLS equation. Secondly, inspired by the form of single-soliton solutions, N-soliton representations of the nonlocal NLS equation are conjectured and then verified via an algebraic proof. Thirdly, to demonstrate the features of the soliton solutions, some special soliton dynamics are theoretically explored and graphically illustrated. The reduction approach proposed in this paper has the merit that it is purely algebraic which does not need to perform complicated spectral analysis of the corresponding Lax pair.

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Acknowledgements

The author is very grateful to the editor and the anonymous referees for their valuable suggestions. The author would also like to thank the support by the Collaborative Innovation Center for Aviation Economy Development of Henan Province.

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  1. School of Science, Zhengzhou University of Aeronautics, Zhengzhou, Henan, 450046, People’s Republic of China

    Jianping Wu

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  1. Jianping Wu
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Wu, J. A novel reduction approach to obtain \({\varvec{N}}\)-soliton solutions of a nonlocal nonlinear Schrödinger equation of reverse-time type. Nonlinear Dyn 106, 775–781 (2021). https://doi.org/10.1007/s11071-021-06813-5

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