An integrable hierarchy associated with loop extension of $\mathbb{Z}_2^2$-graded $\mathfrak{osp}(1|2)$
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911338319577088 |
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| author | Aizawa, N. Fujii, I. Ito, R. |
| author_facet | Aizawa, N. Fujii, I. Ito, R. |
| contents | A hierarchy of $\mathbb{Z}_2^2$-graded integrable equations is constructed using the loop extension of the $\mathbb{Z}_2^2$-graded Lie superalgebra $\mathfrak{osp}(1|2)$. This hierarchy includes $\mathbb{Z}_2^2$-graded extensions of the Liouville, sinh-Gordon, cosh-Gordon, and, in particular, the mKdV equations. The $\mathbb{Z}_2^2$-graded KdV equation is also derived from the $\mathbb{Z}_2^2$-mKdV equation via the Miura transformation. We present explicit formulas for the conserved charges of the $\mathbb{Z}_2^2$-KdV and $\mathbb{Z}_2^2$-mKdV equations. A distinctive feature of these $\mathbb{Z}_2^2$-graded integrable systems is the existence of conserved charges with nontrivial grading. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An integrable hierarchy associated with loop extension of $\mathbb{Z}_2^2$-graded $\mathfrak{osp}(1|2)$ Aizawa, N. Fujii, I. Ito, R. Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems A hierarchy of $\mathbb{Z}_2^2$-graded integrable equations is constructed using the loop extension of the $\mathbb{Z}_2^2$-graded Lie superalgebra $\mathfrak{osp}(1|2)$. This hierarchy includes $\mathbb{Z}_2^2$-graded extensions of the Liouville, sinh-Gordon, cosh-Gordon, and, in particular, the mKdV equations. The $\mathbb{Z}_2^2$-graded KdV equation is also derived from the $\mathbb{Z}_2^2$-mKdV equation via the Miura transformation. We present explicit formulas for the conserved charges of the $\mathbb{Z}_2^2$-KdV and $\mathbb{Z}_2^2$-mKdV equations. A distinctive feature of these $\mathbb{Z}_2^2$-graded integrable systems is the existence of conserved charges with nontrivial grading. |
| title | An integrable hierarchy associated with loop extension of $\mathbb{Z}_2^2$-graded $\mathfrak{osp}(1|2)$ |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2512.14108 |