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A novel general nonlocal reverse-time nonlinear Schrödinger equation and its soliton solutions by Riemann–Hilbert method

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Abstract

In this paper, a novel general nonlocal reverse-time nonlinear Schrödinger (NLS) equation involving two real parameters is proposed from a general coupled NLS system by imposing a nonlocal reverse-time constraint. In this sense, the proposed nonlocal equation can govern the nonlinear wave propagations in such physical situations where the two components of the general coupled NLS system are related by the nonlocal reverse-time constraint. Moreover, the proposed nonlocal equation can reduce to a physically significant nonlocal reverse-time NLS equation in the literature. Based on the Riemann–Hilbert (RH) method, we also explore the complicated symmetry relations of the scattering data underlying the proposed nonlocal equation induced by the nonlocal reverse-time constraint, from which three types of soliton solutions are successfully obtained. Furthermore, some specific soliton dynamical behaviors underlying the obtained solutions are theoretically explored and graphically illustrated.

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Acknowledgements

The author expresses sincere thanks 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, 450046, Henan, China

    Jianping Wu

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Wu, J. A novel general nonlocal reverse-time nonlinear Schrödinger equation and its soliton solutions by Riemann–Hilbert method. Nonlinear Dyn 111, 16367–16376 (2023). https://doi.org/10.1007/s11071-023-08676-4

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