Strachan, I.A.B. (1999) Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations. Journal of Mathematical Physics, 40(10), pp. 5058-5079. (doi: 10.1063/1.533015)
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Abstract
The bi-Hamiltonian structure of certain multicomponent integrable systems, generalizations of the dispersionless Toda hierarchy, is studied 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 that defines the Hamiltonian structure has a 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 extended to include degenerate bi-Hamiltonian structures, such as those given in the first part of the paper, is given.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Strachan, Professor Ian |
| Authors: | Strachan, I.A.B. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Mathematical Physics |
| Publisher: | AIP Publishing |
| ISSN: | 0022-2488 |
| ISSN (Online): | 1089-7658 |
| Published Online: | 23 September 1999 |
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