Geometric aspects of non-homogeneous 1+0 operators
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915893819211776 |
|---|---|
| author | Dell'Atti, Marta Rizzo, Alessandra Vergallo, Pierandrea |
| author_facet | Dell'Atti, Marta Rizzo, Alessandra Vergallo, Pierandrea |
| contents | Led by the key example of the Korteweg-de Vries equation, we study pairs of Hamiltonian operators which are non-homogeneous and are given by the sum of a first-order operator and an ultralocal structure. We present a complete classification of the Casimir functions associated with the degenerate operators in two and three components. We define tensorial criteria to establish the compatibility of two non-homogeneous operators and show a classification of pairs for systems in two components, with some preliminary results for three components as well. Lastly, we study pairs composed of non-degenerate operators only, introducing the definition of bi-pencils. First results show that the considered operators can be related to Nijenhuis geometry, proving a compatibility result in this direction in the framework of Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric aspects of non-homogeneous 1+0 operators Dell'Atti, Marta Rizzo, Alessandra Vergallo, Pierandrea Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems Led by the key example of the Korteweg-de Vries equation, we study pairs of Hamiltonian operators which are non-homogeneous and are given by the sum of a first-order operator and an ultralocal structure. We present a complete classification of the Casimir functions associated with the degenerate operators in two and three components. We define tensorial criteria to establish the compatibility of two non-homogeneous operators and show a classification of pairs for systems in two components, with some preliminary results for three components as well. Lastly, we study pairs composed of non-degenerate operators only, introducing the definition of bi-pencils. First results show that the considered operators can be related to Nijenhuis geometry, proving a compatibility result in this direction in the framework of Lie algebras. |
| title | Geometric aspects of non-homogeneous 1+0 operators |
| topic | Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.21917 |