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PreprintCC BY-NC-SA 4.0arXiv

An integrable deformation of the sine(sinh)-Gordon model -- Non-Lie algebra

  • Meseret Asrat
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Abstract

In this paper we present an integrable model in two dimensions. It is a deformation of the sine(sinh)-Gordon model. We give its Lax connection. We also obtain its (classical) r-matrix. It satisfies the classical Yang-Baxter equation. Thus, the model is a classical integrable field theory in two dimensions. The underlying algebra is a cal Z-graded non-Lie alternative Akivis algebra. An alternative Akivis algebra is the tangent space at the identity of an analytic alternative loop as a Lie algebra is the tangent space at the identity of a Lie group. We expect the model to be integrable at the quantum level. We also give a family of classically integrable models which are related to the Poisson-Boltzmann equation in two dimensions.

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Cite

BibTeXRIS
BibTeX
@misc{asrat2026integrable,
  title = {{An integrable deformation of the sine(sinh)-Gordon model -- Non-Lie algebra}},
  author = {Meseret Asrat},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.15794},
  eprint = {2606.15794},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.15794},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - An integrable deformation of the sine(sinh)-Gordon model -- Non-Lie algebra
AU  - Meseret Asrat
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2606.15794
UR  - https://arxiv.org/abs/2606.15794
AB  - In this paper we present an integrable model in two dimensions. It is a deformation of the sine(sinh)-Gordon model. We give its Lax connection. We also obtain its (classical) r-matrix. It satisfies the classical Yang-Baxter equation. Thus, the model is a classical integrable field theory in two dimensions. The underlying algebra is a cal Z-graded non-Lie alternative Akivis algebra. An alternative Akivis algebra is the tangent space at the identity of an analytic alternative loop as a Lie algebra is the tangent space at the identity of a Lie group. We expect the model to be integrable at the quantum level. We also give a family of classically integrable models which are related to the Poisson-Boltzmann equation in two dimensions.
ER  -