Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866916188024471552 |
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| author | Sakhnovich, Alexander |
| author_facet | Sakhnovich, Alexander |
| contents | We construct so called Darboux matrices and fundamental solutions in the important case of the generalised Hamiltonian (or canonical) systems depending rationally on the spectral parameter. A wide class of explicit solutions is obtained in this way. Interesting results for dynamical systems depending on several variables and their explicit solutions follow. For these purposes we use our version of Bäcklund-Darboux transformation and square roots of the corresponding generalised matrix eigenvalues. Some new auxiliary results on the roots of matrices are included as well. An appendix is added to make the paper self-sufficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_00435 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications Sakhnovich, Alexander Classical Analysis and ODEs Mathematical Physics Dynamical Systems Functional Analysis Spectral Theory 34B30, 34C14, 37C79, 37J06, 15A15 We construct so called Darboux matrices and fundamental solutions in the important case of the generalised Hamiltonian (or canonical) systems depending rationally on the spectral parameter. A wide class of explicit solutions is obtained in this way. Interesting results for dynamical systems depending on several variables and their explicit solutions follow. For these purposes we use our version of Bäcklund-Darboux transformation and square roots of the corresponding generalised matrix eigenvalues. Some new auxiliary results on the roots of matrices are included as well. An appendix is added to make the paper self-sufficient. |
| title | Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications |
| topic | Classical Analysis and ODEs Mathematical Physics Dynamical Systems Functional Analysis Spectral Theory 34B30, 34C14, 37C79, 37J06, 15A15 |
| url | https://arxiv.org/abs/2107.00435 |