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PreprintarXiv licencearXiv

Explicit quasi-periodic solutions to the discrete derivative nonlinear Schrödinger equation

  • Xiaoxue Xu
  • Wei Liu
  • Junyi Zhu
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Abstract

Quasi-periodic solutions to the discrete derivative nonlinear Schrödinger equation are investigated. A Lax pair of the discrete integrable equation is derived, by which we obtain a nonlinear integrable symplectic map. Resorting to this map, the Riemann theta function expressions for discrete potentials are calculated. Consequently, we get the explicit solutions for the discrete derivative nonlinear Schrödinger equation, whose quasi-periodic properties are illustrated through the cases of genus one and genus two.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026explicit,
  title = {{Explicit quasi-periodic solutions to the discrete derivative nonlinear Schrödinger equation}},
  author = {Xiaoxue Xu and Wei Liu and Junyi Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31347},
  eprint = {2610.31347},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31347},
}
RIS
TY  - UNPB
TI  - Explicit quasi-periodic solutions to the discrete derivative nonlinear Schrödinger equation
AU  - Xiaoxue Xu
AU  - Wei Liu
AU  - Junyi Zhu
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31347
UR  - https://arxiv.org/abs/2610.31347
AB  - Quasi-periodic solutions to the discrete derivative nonlinear Schrödinger equation are investigated. A Lax pair of the discrete integrable equation is derived, by which we obtain a nonlinear integrable symplectic map. Resorting to this map, the Riemann theta function expressions for discrete potentials are calculated. Consequently, we get the explicit solutions for the discrete derivative nonlinear Schrödinger equation, whose quasi-periodic properties are illustrated through the cases of genus one and genus two.
ER  -