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Riemann–Hilbert method and multi-soliton solutions of the Kundu-nonlinear Schrödinger equation

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Abstract

In this work, we study the Kundu-nonlinear Schrödinger (Kundu-NLS) equation (so-called the extended NLS equation), which can describe the propagation of the waves in dispersive media. A Lax spectral problem is used to construct the Riemann–Hilbert problem, via a matrix transformation. Based on the inverse scattering transformation, the general solutions of the Kundu-NLS equation are calculated. In the reflection-less case, the special matrix Riemann–Hilbert problem is carefully proposed to derive the multi-soliton solutions. Finally, some novel dynamics behaviors of the nonlinear system are theoretically and graphically discussed.

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Acknowledgements

We are grateful to the reviewers for their encouraging suggestions that were helpful in improving this paper further. This research was supported by the Major Program of Natural Science Foundation of Anhui Higher Institutions under Grant No. KJ2020ZD008.

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  1. School of Mathematical Sciences, Huaibei Normal University, Huaibei, 235000, People’s Republic of China

    Xue-Wei Yan

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Yan, XW. Riemann–Hilbert method and multi-soliton solutions of the Kundu-nonlinear Schrödinger equation. Nonlinear Dyn 102, 2811–2819 (2020). https://doi.org/10.1007/s11071-020-06102-7

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