Mike Hay 2007 J. Phys. A: Math. Theor. 40 10457 doi:10.1088/1751-8113/40/34/005
Mike Hay
Show affiliationsWe present two hierarchies of nonlinear, integrable q-difference equations, one of which includes a q-difference form of each of the second and fifth Painlevé equations,
and
, the other includes
. All the equations have multiple free parameters. A method to calculate a 2 × 2 Lax pair for each equation in the hierarchy is also given.
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
37K60 Lattice dynamics (See also 37L60)
34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
Issue 34 (24 August 2007)
Received 27 May 2007, in final form 17 July 2007
Published 7 August 2007
Mike Hay 2007 J. Phys. A: Math. Theor. 40 10457
Samuel L Braunstein 1998 J. Phys. A: Math. Gen. 31 5767
Ricardo A. Flores et al. 2000 ApJ 535 555
A Kimoto et al 2007 Meas. Sci. Technol. 18 3523
Marco Zoli and A N Das 2004 J. Phys.: Condens. Matter 16 3597
S Emura et al 2009 J. Phys.: Conf. Ser. 190 012102
O Jennrich et al 2001 Class. Quantum Grav. 18 4159
Chiho Matsumoto et al. 2004 ApJ 603 456
Bruce G. Elmegreen 1997 ApJ 480 674
Xu Jie et al 2006 Chinese Phys. Lett. 23 2819