Hamiltonian systems with several space variables: dressing, explicit solutions and energy relations
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866918471204339712 |
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| author | Sakhnovich, Alexander |
| author_facet | Sakhnovich, Alexander |
| contents | We construct so-called Darboux transformations and solutions of the dynamical Hamiltonian systems with several space variables $\frac{\partial ψ}{\partial t}=\sum_{k=1}^r H_k(t)\frac{\partial ψ}{\partial ζ_k}\,$ $( H_k(t)= H_k(t)^*)$. In particular, such systems are analogs of the port-Hamiltonian systems in the important and insufficiently studied case of several space variables. The corresponding energy relations are written down. The method is illustrated by several examples, where explicit solutions are given. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_17492 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hamiltonian systems with several space variables: dressing, explicit solutions and energy relations Sakhnovich, Alexander Dynamical Systems Analysis of PDEs Optimization and Control 37J06, 37N35, 70S10 We construct so-called Darboux transformations and solutions of the dynamical Hamiltonian systems with several space variables $\frac{\partial ψ}{\partial t}=\sum_{k=1}^r H_k(t)\frac{\partial ψ}{\partial ζ_k}\,$ $( H_k(t)= H_k(t)^*)$. In particular, such systems are analogs of the port-Hamiltonian systems in the important and insufficiently studied case of several space variables. The corresponding energy relations are written down. The method is illustrated by several examples, where explicit solutions are given. |
| title | Hamiltonian systems with several space variables: dressing, explicit solutions and energy relations |
| topic | Dynamical Systems Analysis of PDEs Optimization and Control 37J06, 37N35, 70S10 |
| url | https://arxiv.org/abs/2210.17492 |