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Discrete four-component massive Thirring model

  • Xiao-gang Mu
  • Jing Wang
  • Song-lin Zhao
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Abstract

We construct a discrete four-component massive Thirring model (MTM) within the Cauchy matrix framework. A connection between the dependent variables of the discrete four-component MTM and those of the discrete Mikhailov model is established. Taking two successive continuum limits, we first reduce this discrete four-component MTM to its semi-discrete counterpart, and further arrive at the continuous four-component MTM. Solving the determining equation set enables us to construct AKNS-type and KP-type solutions, including explicit soliton solutions and multiple-pole solutions. Imposing the local reduction and nonlocal reduction on the discrete four-component MTM yields the discrete MTM and the reverse-(n,m) discrete MTM, respectively. For these two reduced systems, we prove that the former admits AKNS-type solutions, whereas the latter possesses both AKNS-type and KP-type solutions.

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Cite

BibTeXRIS
BibTeX
@misc{mu2026discrete,
  title = {{Discrete four-component massive Thirring model}},
  author = {Xiao-gang Mu and Jing Wang and Song-lin Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07686},
  eprint = {2611.07686},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07686},
}
RIS
TY  - UNPB
TI  - Discrete four-component massive Thirring model
AU  - Xiao-gang Mu
AU  - Jing Wang
AU  - Song-lin Zhao
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07686
UR  - https://arxiv.org/abs/2611.07686
AB  - We construct a discrete four-component massive Thirring model (MTM) within the Cauchy matrix framework. A connection between the dependent variables of the discrete four-component MTM and those of the discrete Mikhailov model is established. Taking two successive continuum limits, we first reduce this discrete four-component MTM to its semi-discrete counterpart, and further arrive at the continuous four-component MTM. Solving the determining equation set enables us to construct AKNS-type and KP-type solutions, including explicit soliton solutions and multiple-pole solutions. Imposing the local reduction and nonlocal reduction on the discrete four-component MTM yields the discrete MTM and the reverse-(n,m) discrete MTM, respectively. For these two reduced systems, we prove that the former admits AKNS-type solutions, whereas the latter possesses both AKNS-type and KP-type solutions.
ER  -