dorsal/arxiv
View SchemaDegenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
| Authors | I. A. B. Strachan |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9807004 |
| URL | https://arxiv.org/abs/solv-int/9807004 |
| DOI | 10.1063/1.533015 |
| Journal | J. Math. Phys. 40, 5058 (1999); |
Abstract
The bi-Hamiltonian structure of certain multi-component integrable systems, generalizations of the dispersionless Toda hierarchy, is studies for systems derived from a rational Lax function. One consequence of having a rational rather than a polynomial Lax function is that the corresponding bi-Hamiltonian structures are degenerate, i.e. the metric which defines the Hamiltonian structure has vanishing determinant. Frobenius manifolds provide a natural setting in which to study the bi-Hamiltonian structure of certain classes of hydrodynamic systems. Some ideas on how this structure may be extanded to include degenerate bi-Hamiltonian structures, such as those given in the first part of the paper, are given.
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"abstract": "The bi-Hamiltonian structure of certain multi-component integrable systems,\ngeneralizations of the dispersionless Toda hierarchy, is studies for systems\nderived from a rational Lax function. One consequence of having a rational\nrather than a polynomial Lax function is that the corresponding bi-Hamiltonian\nstructures are degenerate, i.e. the metric which defines the Hamiltonian\nstructure has vanishing determinant. Frobenius manifolds provide a natural\nsetting in which to study the bi-Hamiltonian structure of certain classes of\nhydrodynamic systems. Some ideas on how this structure may be extanded to\ninclude degenerate bi-Hamiltonian structures, such as those given in the first\npart of the paper, are given.",
"arxiv_id": "solv-int/9807004",
"authors": [
"I. A. B. Strachan"
],
"categories": [
"solv-int",
"nlin.SI"
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"doi": "10.1063/1.533015",
"journal_ref": "J. Math. Phys. 40, 5058 (1999);",
"title": "Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations",
"url": "https://arxiv.org/abs/solv-int/9807004"
},
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