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A binary Darboux transformation for multicomponent NLS equations and their reductions

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Abstract

We present a binary Darboux transformation for multicomponent NLS equations and their reduced integrable counterparts. The starting point is to apply two pairs of eigenfunctions and adjoint eigenfunctions, and the resulting binary Darboux transformation can be decomposed into an N-fold Darboux transformation. By taking the zero potential as a seed solution, soliton solutions are generated from the binary Darboux transformation for multicomponent NLS equations and their reductions.

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Acknowledgements

The work was supported in part by NSFC under the grants 11975145 and 11972291. The authors would also like to thank Alle Adjiri, Ahmed Ahmed, Yushan Bai, Qingxian Chen, Yehui Huang, Yan Jiang, Wenting Li, and Morgan McAnally, Fudong Wang and Yong Zhang for their valuable discussions.

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Authors and Affiliations

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

    Wen-Xiu Ma

  2. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    Wen-Xiu Ma & Sumayah Batwa

  3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Wen-Xiu Ma

  4. School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

    Wen-Xiu Ma

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  1. Wen-Xiu Ma
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  2. Sumayah Batwa
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Correspondence to Wen-Xiu Ma.

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Ma, WX., Batwa, S. A binary Darboux transformation for multicomponent NLS equations and their reductions. Anal.Math.Phys. 11, 44 (2021). https://doi.org/10.1007/s13324-021-00477-5

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