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A vectorial Darboux transformation for the Fokas–Lenells system

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  • Ye, Rusuo
  • Zhang, Yi

Abstract

We first reveal that there is a Riccati-type Miura transformation from the Fokas–Lenells (FL) system to the first member of the negative part of the AKNS hierarchy. We derive a vectorial Darboux transformation for the FL system by using the bidifferential graded algebra approach. Two types of reductions lead to the FL equation and nonlocal FL (nFL) equation, respectively. From vanishing seed solutions, N-soliton solutions for the FL equation and nFL equation are provided, with spectral matrices of the form of diagonal. Finally, as an application, we perform an asymptotic analysis for the bright–bright solitons of the nonlocal case.

Suggested Citation

  • Ye, Rusuo & Zhang, Yi, 2023. "A vectorial Darboux transformation for the Fokas–Lenells system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001340
    DOI: 10.1016/j.chaos.2023.113233
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