Method of ${\cal M}_{n}$-Extension via Frobenius Companion Matrices
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910863929114624 |
|---|---|
| author | Gürses, Metin Pekcan, Aslı |
| author_facet | Gürses, Metin Pekcan, Aslı |
| contents | Frobenius companion matrices arise when we write an $n$-th order linear ordinary differential equation as a system of first order differential equations. These matrices and their transpose have very nice properties. By using the powers of these matrices we form a closed algebra under the matrix multiplication. Structure constants of this commuting algebra are the components of companion matrix. We use these matrices in our method of ${\cal M}_{n}$-extension of scalar integrable equations to produce new systems of integrable equations with recursion operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05635 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Method of ${\cal M}_{n}$-Extension via Frobenius Companion Matrices Gürses, Metin Pekcan, Aslı Exactly Solvable and Integrable Systems Frobenius companion matrices arise when we write an $n$-th order linear ordinary differential equation as a system of first order differential equations. These matrices and their transpose have very nice properties. By using the powers of these matrices we form a closed algebra under the matrix multiplication. Structure constants of this commuting algebra are the components of companion matrix. We use these matrices in our method of ${\cal M}_{n}$-extension of scalar integrable equations to produce new systems of integrable equations with recursion operators. |
| title | Method of ${\cal M}_{n}$-Extension via Frobenius Companion Matrices |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.05635 |