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PreprintCC BY 4.0arXiv

Maps from the Dbar-data to the derivative NLS potentials

  • Junyi Zhu
  • Xueru Wang
  • Huan Liu
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Abstract

We develop a decomposition technique to investigate maps from the Dbar data to the derivative NLS potentials. We define a new integral operator which is equivalent to a modified Dbar problem relevant to the derivative NLS spectral problem, including the Kaup-Newell spectral problem, the Chen-Lee-Liu spectral problem and the Gerdjikov-Ivanov spectral problem. The well-posedness for the integral operator with the kernel eik2xσ3 is discussed via the decomposition technique. Under different constraint conditions, the derivative NLS potentials are reconstructed via the Dbar data. We discuss the symmetry condition of the Dbar data as well as the compatibility of the derivative NLS spectral problem with the modified Dbar problem. We show that the maps from the Dbar data to the derivative NLS potentials are Lipschitz continuous.

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Cite

BibTeXRIS
BibTeX
@misc{zhu2026maps,
  title = {{Maps from the Dbar-data to the derivative NLS potentials}},
  author = {Junyi Zhu and Xueru Wang and Huan Liu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04135},
  eprint = {2611.04135},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04135},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Maps from the Dbar-data to the derivative NLS potentials
AU  - Junyi Zhu
AU  - Xueru Wang
AU  - Huan Liu
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04135
UR  - https://arxiv.org/abs/2611.04135
AB  - We develop a decomposition technique to investigate maps from the Dbar data to the derivative NLS potentials. We define a new integral operator which is equivalent to a modified Dbar problem relevant to the derivative NLS spectral problem, including the Kaup-Newell spectral problem, the Chen-Lee-Liu spectral problem and the Gerdjikov-Ivanov spectral problem. The well-posedness for the integral operator with the kernel e^ik^2xσ_3 is discussed via the decomposition technique. Under different constraint conditions, the derivative NLS potentials are reconstructed via the Dbar data. We discuss the symmetry condition of the Dbar data as well as the compatibility of the derivative NLS spectral problem with the modified Dbar problem. We show that the maps from the Dbar data to the derivative NLS potentials are Lipschitz continuous.
ER  -