MR2108677
Mikio MURATA
Mikio MURATA
New Expressions for Discrete Painlevé Equations
Funkcialaj Ekvacioj. Serio Internacia
47
2004
291--305
http://fe.math.kobe-u.ac.jp/FE/FullPapers/47-2/47_291.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2108677
We present a new expression for the elliptic-difference Painlevé equation. As in our construction all parameters in their equations appear in a symmetric way, the permutation symmetry of the equations is immediately apparent. We present expressions for other discrete Painlevé equations, obtained in a similar way.
Integrable systems, Difference equations, Painlevé-type functions.
39A20, 33E17, 14E07.
47-291
2004
New Expressions for Discrete Painlevé Equations
Mikio MURATA
Mikio MURATA
1
Grammaticos, B.; Ramani, A.; Papageorgiou, V. G.
Do integrable mappings have the Painlevé property?
Phys. Rev. Lett.
67
1991
1825-1828
MR1125950
2
Grammaticos, B.; Ohta, Y.; Ramani, A.; Sakai, H.
Degeneration through coalescence of the $q$-Painlevé VI equation
J. Phys. A: Math. Gen.
31
1998
3545-3558
MR1626199
3
Jimbo, M.; Sakai, H.
A $q$-analog of the sixth Painlevé equation
Lett. Math. Phys.
38
1996
145-154
MR1403067
4
Kajiwara, K.; Masuda, T.; Noumi, M.; Ohta, Y.; Yamada, Y.
${}_{10}E_9$ solution to the elliptic Painlevé equation
J. Phys. A: Math. Gen.
36
2003
L263-L272
MR1984002
5
Murata, M.; Sakai, H.; Yoneda, J.
Riccati solutions of discrete Painlevé equations with Weyl group symmetry of type $E_8^{(1)}$
J. Math. Phys.
44
2003
1396-1414
MR1958273
6
Ohta, Y.; Ramani, A.; Grammaticos, B.
An affine Weyl group approach to the eight-parameter discrete Painlevé equation
J. Phys. A: Math. Gen.
34
2001
10523-10532
MR1877472
7
Ramani, A.; Grammaticos, B.; Hietarinta, J.
Discrete versions of the Painlevé equations
Phys. Rev. Lett.
67
1991
1829-1832
MR1125951
8
Sakai, H.
Rational Surfaces Associated with Affine Root Systems and Geometry of the Painlevé Equations
Comm. Math. Phys.
220
2001
165-229
MR1882403