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Fokas-Lenells equation dark soliton and gauge equivalent spin equation

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Abstract

We propose the Hirota bilinearization of the Fokas–Lenells derivative nonlinear Schrödinger equation (FLE) with a non-vanishing background. In the proposed method, we have introduced an auxiliary function to transform the equation into bilinear form. The use of an auxiliary function makes the method simpler than the ones reported earlier. Using the proposed method we have obtained the dark (and bright) one soliton solution. We have also discussed the properties of the obtained soliton and mentioned the criteria upon which the nature of the soliton being dark or bright depends upon. Then we have obtained the dark (and bright) two soliton solution and discussed the respective properties and also through asymptotic analysis showed how the phase between the two individual solitons changes before and after interaction. Eventually we have proposed the scheme for obtaining N soliton solutions. The proposed method can be extended to other nonlinear equations where straightforward bilinearization is not feasible. Later, we have introduced a gauge transformation which transforms the spectral problem of FLE into a spectral problem for the Landau–Lifshitz (LL) spin system. Soliton act as an information carrier and LL system exhibits a variety of nonlinear structures so the study is worth doing.

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Acknowledgements

R. Dutta and S. Talukdar acknowledge Department of Science & Technology, Govt. of India for INSPIRE fellowship award. Corresponding award numbers DST/INSPIRE Fellowship/2020/IF200303 and DST/INSPIRE Fellowship/2020/IF200278.

Funding

R. Dutta and S. Talukdar receive fellowship from Department of Science & Technology, Govt. of India under INSPIRE programme. Corresponding fellowship award numbers DST/INSPIRE Fellowship/2020/IF200303 and DST/INSPIRE Fellowship/2020/IF200278. Other than this the authors did not receive any fund support from any organization for the submitted work.

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Author notes

  1. Sagardeep Talukdar, Gautam K. Saharia, Sudipta Nandy have contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, Cotton University, Panbazar, Guwahati, Assam, 781001, India

    Riki Dutta, Sagardeep Talukdar, Gautam K. Saharia & Sudipta Nandy

Authors
  1. Riki Dutta
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  2. Sagardeep Talukdar
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  3. Gautam K. Saharia
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  4. Sudipta Nandy
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Contributions

Conceptualization: All the authors; formal analysis: RD; supervision: SN; validation: SN, ST, GKS; writing - original draft: RD; writing - review & editing: all the authors.

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Correspondence to Sudipta Nandy.

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Dutta, R., Talukdar, S., Saharia, G.K. et al. Fokas-Lenells equation dark soliton and gauge equivalent spin equation. Opt Quant Electron 55, 1183 (2023). https://doi.org/10.1007/s11082-023-05460-x

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