Separable Hamiltonians and integrable systems of hydrodynamic type

Journal of Geometry and Physics

Volumn 21, Issue 2, 1997, Pages 169-182

  Ferapontov, E V ^a   Fordy, A P ^b  

^a INSTITUTE OF MATHEMATICAL MODELING   (Russian Federation)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Hydrodynamics; Integrable systems; Separable Hamiltonians

Indexed keywords

EID: 0030638622     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(96)00013-7     Document Type: Article

References (14)

1. [1] B.A. Dubrovin and S.P. Novikov, Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory, Usp. Math. Nauk 44 (1989) 29-90.
2. [2] L.P. Eisenhart, Riemannian Geometry (Princeton University Press, Princeton, 1926).
3. [3] E.V. Ferapontov, Integration of weakly nonlinear hydrodynamic systems in Riemann invariants, Phys. Letts. A 158 (1991) 112-118.
4. [4] E.V. Ferapontov and A.P. Fordy, Nonhomogeneous systems of hydrodynamic type related to velocity dependent quadratic Hamiltonians, preprint (1995).
5. [5] A.P. Fordy, The Hénon-Heiles system revisited, Physica D 52 (1991) 201-210.
6. [6] J. Gibbons and S.P. Tsarev, Reductions of the Benney equations. Phys. Lett. A 211 (1996) 19-24.
7. [7] C.G. Jacobi, Vorlesungen über dynamic, Gesammelte Werke (Supplementband) (1884) p.212.
8. [8] H. Knörrer, Geodesics on quadrics and a mechanical problem of C. Neumann, J. Reine Angew. Math. 334 (1982) 69-78.
9. [9] C. Neumann, De problemate quodam mechanico, quod ad priman integralium ultraellipticorum classem revocatur, J. Reine Angew. Math. 56 (1859) 46-63.
10. [10] S.P. Tsarev, On Poisson brackets and one-dimensional Hamiltonian systems of hydrodynamic type, Sov. Math. Dokl. 31 (1985) 488-191.
11. [11] S.P. Tsarev, The geometry of Hamiltonian systems of hydrodynamic type. The generalised hodograph transform, USSR Izv. 37 (1991) 397-419.
12. [12] A.P. Veselov, Two remarks about the connection of Jacobi and Neumann integrable systems, Math. Z. 216 (1994) 337-345.
13. [13] O.I. Bogoyavlenskii and S.P. Novikov, The relationship between Hamiltonian formalisms of stationary and nonstationary problems, Func.Anal. Apps. 10 (1976) 8-11.
14. [14] O.I. Mokbov, The Hamiltonian property of an evolutionary flow on the set of stationary points of its integral, Russian Math. Surveys 39 (1984) 133-134.