Painlevé transcendents and Einstein's equation

Classical and Quantum Gravity

Volumn 13, Issue 4, 1996, Pages

  Calvert, G ^a   Woodhouse, N M J ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22244479626     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/13/4/001     Document Type: Article

References (12)

1. Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (LMS Lecture Note Series 149) (Cambridge: Cambridge University Press)
2. Cosgrove C M 1993 Painlevé classification of a class of differential equations of the second order and second degree Stud. Appl Math. 88 25-87
3. Cosgrove C M 1977 New family of exact stationary axisymmetric gravitational fields generalising the Tomimatsu-Sato solutions J. Phys. A: Math. Gen. 10 209-32
4. Chandrasekhar S 1986 Cylindrical waves in general relativity Proc. R. Soc. A 408 209-32
5. Fletcher J and Woodhouse N M J 1990 Twistor characterization of stationary axisymmetric solutions of Einstein's equations Twisters in Mathematics and Physics (LMS Lecture Note Series 156) ed T N Bailey and R J Baston (Cambridge: Cambridge University Press)
6. Lukashevich N A and Yablonskii A I 1967 On a set of solutions of the sixth Painlevé equation Differentsial'nye Urauneniya 3 520-3
7. Léauté B and Marcilhacy G 1979 Sur certaines solutions particulières transcendantes des équations d'Einstein Ann. Inst. Henri Poincaré A 31 363-75
8. Mason L J and Woodhouse N M J 1993 Self-duality and the Painlevé transcendents Nonlinearity 6 569-81
9. Mason L J and Woodhouse N M J 1996 Twistor Theory, Self-duality, and Integrability (Oxford: Oxford University Press)
10. Persides S and Xanthopoulos B C 1988 Some new stationary axisymmetric asymptotically flat spacetimes obtained from Painlevé transcendents J. Math. Phys. 29 674-80
11. Ward R S 1983 Stationary axisymmetric spacetimes: a new approach Gen. Rel. Grav. 15 105-9
12. Witten L 1979 Static axially symmetric solutions of self-dual SU(2) gauge fields in Euclidean four-dimensional space Phys. Rev. D 19 718-20