Degenerate bi-Hamiltonian structures of the hydrodynamic type
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 2, pp. 294-304 Cet article a éte moissonné depuis la source Math-Net.Ru

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Degenerate bi-Hamiltonian Poisson brackets of the hydrodynamic type are studied. They are bi-Hamiltonian structures of certain dispersionless rational Lax equations and are related to the notion of a degenerate Frobenius manifold.
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I. A. Strachan. Degenerate bi-Hamiltonian structures of the hydrodynamic type. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 2, pp. 294-304. http://geodesic.mathdoc.fr/item/TMF_2000_122_2_a11/

[1] B. Dubrovin, S. P. Novikov, DAN SSSR, 270 (1983), 781–785 | MR | Zbl

[2] N. I. Grinberg, UMN, 40:4 (1985), 217–218 | MR | Zbl

[3] O. I. Mokhov, Phys. Lett. A, 166 (1992), 215–216 | DOI | MR

[4] I. Dorfmann, Dirac Structures and Integrability of Nonlinear Evolution Equations, Wiley, N. Y., 1993 | MR

[5] B. Dubrovin, “Geometry of 2D topological field theories”, Integrable Systems and Quantum Groups, Lectures Given at the 1st Session of the Centro Internazionale Matematico Estivo (CIME) (Montecatini Terme, Italy, June 14–22, 1993), Springer Lecture Notes in Math., 1620, eds. M. Francaviglia, S. Greco, Springer, Berlin, 1996, 120–3348 | DOI | MR

[6] F. Magri, J. Math. Phys., 19 (1978), 1156–1162 | DOI | MR | Zbl

[7] O. I. Mokhov, UMN, 52:6 (1997), 171–172 | DOI | MR

[8] O. I. Mokhov, UMN, 53:2 (1998), 153–154 | DOI | MR | Zbl

[9] B. Dubrovin, Y. Zhang, Compos. Math., 111:2 (1998), 167–219 | DOI | MR | Zbl

[10] I. A. B. Strachan, J. Math. Phys., 40 (1999), 5058–5079 | DOI | MR | Zbl

[11] D. B. Fairlie, I. A. B. Strachan, Inverse problems, 12 (1996), 885–908 | DOI | MR | Zbl

[12] Y. Kodama, Private communication and seminar given at the ICMS (Edinburgh, Sept. 1998)

[13] S. Aoyama, Y. Kodama, Commum. Math. Phys., 182 (1996), 185–219 | DOI | MR | Zbl

[14] M. V. Polyak, UMN, 42:3 (1987), 195–196 | MR