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General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

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Abstract

The inverse scattering transformation for a novel nonlocal Lakshmanan–Porsezian–Daniel (LPD) equation with rapidly decaying initial data is studied in the framework of Riemann–Hilbert problem. Firstly, a novel integrable nonlocal LPD equation corresponding to a \(3\times 3\) Lax pair is proposed. Secondly, the inverse scattering process with a novel left-right \(3\times 3\) matrix Riemann–Hilbert(RH) problem is constructed. The analytical properties and symmetry relations for the Jost functions and scattering data are considerably different from the local ones. Due to the special symmetry properties for the nonlocal LPD equation, the zeros of the RHP problem are purely imaginary or occur in pairs. With different types and configuration of zeros, the soliton formula is provided and the rich dynamical behaviors for the three kinds of multi-solitons for the novel nonlocal LPD equation are demonstrated. Third, by a technique of adding perturbed parameters and limiting process, the formula of higher-order solitons for the nonlocal LPD equation is exhibited. Lastly, the plots of diverse higher-order solitons and various solutions corresponding to different combinations of the following zeros: purely imaginary higher-order zeros, purely imaginary simple zeros, pairs of non-purely imaginary simple zeros and pairs of non-purely imaginary higher-order zeros are displayed.

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Data Availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The project is supported by the Future Scientist and Outstanding Scholar Cultivation Program of East China Normal University (No.WLKXJ202001), National Natural Science Foundation of China (No.12175069, 12235007) and Science and Technology Commission of Shanghai Municipality (No.21JC1402500 and No.18dz2271000).

Funding

The work is supported by the Future Scientist and Outstanding Scholar Cultivation Program of East China Normal University (No.WLKXJ202001), National Natural Science Foundation of China (No.12175069, 12235007) and Science and Technology Commission of Shanghai Municipality (No.21JC1402500 and No.18dz2271000).

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200241, China

    Minmin Wang

  2. Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, School of Mathematical Sciences, East China Normal University, Shanghai, 200241, China

    Yong Chen

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Yong Chen

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  1. Minmin Wang
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  2. Yong Chen
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All authors contributed to the study conception and theory. Calculation and analysis were performed by Wang Minmin. The first draft of the manuscript was written by Wang Minmin. All authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Yong Chen.

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The work is supported by the Future Scientist and Outstanding Scholar Cultivation Program of East China Normal University (No.WLKXJ202001), National Natural Science Foundation of China(No.12175069) and Science and Technology Commission of Shanghai Municipality (No.21JC1402500 and No.18dz2271000)

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Wang, M., Chen, Y. General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation. Nonlinear Dyn 111, 655–669 (2023). https://doi.org/10.1007/s11071-022-07844-2

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