N Joshi and M Mazzocco 2003 Nonlinearity 16 427 doi:10.1088/0951-7715/16/2/304
N Joshi1 and M Mazzocco2,3
Show affiliationsRecommended by P Deift
The first five classical Painlevé equations are known to have solutions described by divergent asymptotic power series near infinity. Here, we prove that such solutions also exist for the infinite hierarchy of equations associated with the second Painlevé equation. Moreover, we prove that these are unique in certain sectors near infinity.
34M30 Asymptotics, summation methods
34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
Issue 2 (March 2003)
Received 29 May 2002, in final form 1 November 2002
Published 18 December 2002
N Joshi and M Mazzocco 2003 Nonlinearity 16 427
U Saha and R Ghosh 1999 J. Phys. D: Appl. Phys. 32 820
A N F Aleixo et al 2000 J. Phys. A: Math. Gen. 33 1503
Z Jiang et al 2009 Metrologia 46 214
Apollo Segal 1999 J. Phys. D: Appl. Phys. 32 991
Ken Kamrin et al 2007 Modelling Simul. Mater. Sci. Eng. 15 S449
Rostislav V Lapshin 2004 Nanotechnology 15 1135
D Liu et al 2004 J. Micromech. Microeng. 14 567
A Picard 2006 Metrologia 43 46
I Sauers and G Harman 1992 J. Phys. D: Appl. Phys. 25 761