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Dynamic behaviors of soliton solutions for a three-coupled Lakshmanan–Porsezian–Daniel model

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Abstract

In this paper, we use the Riemann–Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan–Porsezian–Daniel (LPD) model, which describes the dynamics of alpha helical protein with the interspine coupling at the fourth-order dispersion term. Through the spectral analysis of Lax pair, we construct the higher-order matrix RH problem for the three-coupled LPD model, when the jump matrix of this particular RH problem is a \(4\times 4\) unit matrix, the exact N-soliton solutions of the three-coupled LPD model can be exhibited. As special examples, we also investigate the nonlinear dynamical behaviors of the single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an integrable generalized N-component LPD model with its linear spectral problem is discussed.

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Acknowledgements

The authors would like to express our sincere thanks to every member in our discussion group for their valuable comments.

Funding

This study was funded by National Natural Science Foundation of China (grant numbers 12147115, 11835011 and 11975145), by Natural Science Foundation of Anhui Province (grant number 2108085QA09), by Postdoctoral Fund of Zhejiang Normal University (grant number ZC304021909), by Key Projects of Natural Science Research in Colleges and Universities in Anhui Province (grant number KJ2021B03).

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Authors and Affiliations

  1. Department of Physics, Zhejiang Normal University, Jinhua, 321004, China

    Bei-Bei Hu & Ji Lin

  2. School of Mathematics and Finance, Chuzhou University, Anhui, 239000, China

    Bei-Bei Hu & Ling Zhang

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  1. Bei-Bei Hu
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  2. Ji Lin
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Hu, BB., Lin, J. & Zhang, L. Dynamic behaviors of soliton solutions for a three-coupled Lakshmanan–Porsezian–Daniel model. Nonlinear Dyn 107, 2773–2785 (2022). https://doi.org/10.1007/s11071-021-07135-2

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  • DOI: https://doi.org/10.1007/s11071-021-07135-2

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