Hydrodynamic reductions of the heavenly equation

Classical and Quantum Gravity

Volumn 20, Issue 11, 2003, Pages 2429-2441

  Ferapontov, E V ^a   Pavlov, M V ^a  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037534179     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/20/11/331     Document Type: Article

References (26)

1. Penrose R 1976 Nonlinear gravitons and curved twistor theory Gen. Rel. Grav. 7 31-52
2. Plebański J F 1975 Some solutions of complex Einstein equations J. Math. Phys. 16 2395-402
3. Ko M, Ludvigsen M, Newman E T and Tod K P 1981 The theory of ℋ-space Phys. Rep. 71 51-139
4. Boyer C P and Winternitz P 1989 Symmetries of the self-dual Einstein equations: I. The infinite-dimensional symmetry group and its low-dimensional subgroups J. Math. Phys. 30 1081-94
5. Strachan IA B 1993 Hierarchy of conservation laws for self-dual gravity Class. Quantum Grav. 10 1417-23
6. Strachan IA B 1995 The symmetry structure of the anti-self-dual Einstein hierarchy J. Math. Phys. 36 3566-73
7. Nutku Y and Sheftel M B 2001 Differential invariants and group foliation for the complex Monge-Ampre equation J. Phys. A: Math. Gen. 34 137-56
8. Boyer C P and Plebański J F 1985 An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces J. Math. Phys. 26 229-34
9. Popov A D, Bordemann M and Römer H 1996 Symmetries, currents and conservation laws of self-dual gravity Phys. Lett. B 385 63-74
10. Lechtenfeld O and Popov A D 2000 Closed N = 2 strings: picture-changing, hidden symmetries and SDG hierarchy Int. J. Mod. Phys. A 15 4191-236
11. Dunajski M and Mason L J 2003 Twistor theory of hyper-Kähler metrics with hidden symmetries Preprint math.DG/0301171
12. Boyer C P, Finley J D and Plebański J F 1980 Complex general relativity, ℋ and ℋℋ spaces - a survey of one approach General Relativity and Gravitation vol 2 (New York: Plenum) pp 241-81
13. Gibbons J and Kodama Y 1989 A method for solving the dispersionless KP hierarchy and its exact solutions: II Phys. Lett. A 135 167-70
14. Gibbons J and Tsarev S P 1996 Reductions of the Benney equations Phys. Lett. A 211 19-24
15. Gibbons J and Tsarev S P 1999 Conformal maps and reductions of the Benney equations Phys. Lett. A 258 263-71
16. Yu Lei 2001 Reductions of dispersionless integrable hierarchies PhD Thesis Imperial College, London
17. Manas M, Martinez Alonso L and Medina E 2002 Reductions and hodograph solutions of the dispersionless KP hierarchy J. Phys. A: Math. Gen. 35 401-17
18. Manas M and Martinez Alonso L 2002 A hodograph transformation which applies to the heavenly equation Preprint nlin. SI/0209050
19. Guil F, Manas M and Martinez Alonso L 2002 On the Whitham hierarchies: reductions and hodograph solutions Preprint nlin.SI/0209051
20. Ferapontov E V, Korotkin D A and Shramchenko V A 2002 Boyer-Finley equation and systems of hydrodynamic type Class. Quantum Grav. 19 L1-L6
21. Tsarev S P 1991 The geometry of Hamiltonian systems of hydrodynamic type: the generalized hodograph method Math. USSR Izv. 37 397-419
22. Dubrovin B A and Novikov S P 1989 Hydrodynamics of weakly deformed soliton lattices: differential geometry and Hamiltonian theory Russ. Math. Surv. 44 35-124
23. Dubrovin B A 1996 Geometry of 2D Topological Field Theories (Lecture Notes in Mathematics vol 1620) (Berlin: Springer) pp 120-348
24. Pavlov M V and Tsarev S P 2003 Three-Hamiltonian structures of the Egorov systems of hydrodynamic type Funct. Anal. Appl. 37 32-45
25. Boyer C P and Finley J D 1982 III Killing vectors in self-dual, Euclidean Einstein spaces J. Math. Phys. 23 1126-30
26. Finley J D and Plebański J F 1979 The classification of ℋ-spaces admitting a Killing vector J. Math. Phys. 20 1938-45