Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911837753180160 |
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| author | Kassotakis, Pavlos |
| author_facet | Kassotakis, Pavlos |
| contents | We present two non-equivalent families of hierarchies of non-Abelian compatible maps and we provide their Lax pair formulation. These maps are associated with families of hierarchies of non-Abelian Yang-Baxter maps, which we provide explicitly. In addition, these hierarchies correspond to integrable difference systems with variables defined on edges of an elementary cell of the $\mathbb{Z}^2$ graph, that in turn lead to hierarchies of difference systems with variables defined on vertices of the same cell. In that respect we obtain the non-Abelian lattice-modified Gel'fand-Dikii hierarchy, together with the explicit form of a non-Abelian hierarchy that we refer to as the lattice-NQC (or lattice-$(Q3)_0$) Gel'fand-Dikii hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03412 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps Kassotakis, Pavlos Exactly Solvable and Integrable Systems 37K60, 39A14, 37K10, 16T25 We present two non-equivalent families of hierarchies of non-Abelian compatible maps and we provide their Lax pair formulation. These maps are associated with families of hierarchies of non-Abelian Yang-Baxter maps, which we provide explicitly. In addition, these hierarchies correspond to integrable difference systems with variables defined on edges of an elementary cell of the $\mathbb{Z}^2$ graph, that in turn lead to hierarchies of difference systems with variables defined on vertices of the same cell. In that respect we obtain the non-Abelian lattice-modified Gel'fand-Dikii hierarchy, together with the explicit form of a non-Abelian hierarchy that we refer to as the lattice-NQC (or lattice-$(Q3)_0$) Gel'fand-Dikii hierarchy. |
| title | Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps |
| topic | Exactly Solvable and Integrable Systems 37K60, 39A14, 37K10, 16T25 |
| url | https://arxiv.org/abs/2202.03412 |