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The exact solutions to a new type space reverse nonlocal Lakshmanan–Porserzian–Daniel equation

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Abstract

In this paper, we study a new type space reverse nonlocal Lakshmanan–Porserzian–Daniel (LPD) equation which can be derived from the two-component LPD system with a special reduction. We construct the multi-fold binary Darboux transformation for the nonlocal equation. The advantage of the binary Darboux transformation is that it provide a short-cut to construct explicit formulas for the solutions of nonlocal equation with zero and non-zero background conditions, such as the interaction bright soliton wave which can degenerate into the one bright wave having a sudden phase shift, the bound state bright wave which looks like a breather wave, the multi-humps bright wave, the interaction breather wave and the resonance breather wave. We find that these solutions exhibit various dynamic evolutions, and most of the collisions between the waves in these solutions are inelastic.

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Funding

The work of Song is supported by National Natural Science Foundation of China (Grant No. 11801367), Zhang is supported by Science and Technology Projects in Guangzhou (Grant NO.202102021152), and Zhao is supported by Natural Science Foundation of Shanghai (Grant No. 20ZR1421900) and National Natural Science Foundation of China (Grant No. 11301331).

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, 516 Jungong Road, Shanghai, 200093, People’s Republic of China

    Caiqin Song & Ri-Rong Fang

  2. Department of Humanities and Social Sciences, Guangzhou Maritime University, 101 Hongshan SAN Road, Guangzhou, 510725, People’s Republic of China

    Hui-Li Zhang

  3. School of Statistics and Information, Shanghai University of International Business and Economics, 1900 Wenxiang Road, Shanghai, 201620, People’s Republic of China

    Hai-qiong Zhao

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  1. Caiqin Song
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Correspondence to Hai-qiong Zhao.

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Song, C., Fang, RR., Zhang, HL. et al. The exact solutions to a new type space reverse nonlocal Lakshmanan–Porserzian–Daniel equation. Nonlinear Dyn 112, 591–599 (2024). https://doi.org/10.1007/s11071-023-09057-7

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  • DOI: https://doi.org/10.1007/s11071-023-09057-7

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