dorsal/arxiv
View SchemaThe separability and dynamical $r$-matrix for the constrained flows of Jaulent-Miodek hierarchy
| Authors | Yunbo Zeng |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9509009 |
| URL | https://arxiv.org/abs/solv-int/9509009 |
Abstract
We show here the separability of Hamilton-Jacobi equation for a hierarchy of integrable Hamiltonian systems obtained from the constrained flows of the Jaulent-Miodek hierarchy. The classical Poisson structure for these Hamiltonian systems is constructed. The associated $r$-matrices depend not only on the spectral parameters, but also on the dynamical variables and, for consistency, have to obey the classical Yang-Baxter equations of dynamical type. Some new solutions of classical dynamical Yang-Baxter equations are presented. Thus these integrable systems provide examples both for the dynamical $r$-matrix and for the separable Hamiltonian system not having a natural Hamiltonian form.
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"abstract": "We show here the separability of Hamilton-Jacobi equation for a hierarchy of\nintegrable Hamiltonian systems obtained from the constrained flows of the\nJaulent-Miodek hierarchy. The classical Poisson structure for these Hamiltonian\nsystems is constructed. The associated $r$-matrices depend not only on the\nspectral parameters, but also on the dynamical variables and, for consistency,\nhave to obey the classical Yang-Baxter equations of dynamical type. Some new\nsolutions of classical dynamical Yang-Baxter equations are presented. Thus\nthese integrable systems provide examples both for the dynamical $r$-matrix and\nfor the separable Hamiltonian system not having a natural Hamiltonian form.",
"arxiv_id": "solv-int/9509009",
"authors": [
"Yunbo Zeng"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "The separability and dynamical $r$-matrix for the constrained flows of Jaulent-Miodek hierarchy",
"url": "https://arxiv.org/abs/solv-int/9509009"
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