TY - JOUR

T1 - A family of solutions of a higher order PVI equation near a regular singularity

AU - Shimomura, Shun

PY - 2006/9/29

Y1 - 2006/9/29

N2 - Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlevé equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N ≤ 2.

AB - Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlevé equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N ≤ 2.

UR - http://www.scopus.com/inward/record.url?scp=33748773348&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748773348&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/39/39/S09

DO - 10.1088/0305-4470/39/39/S09

M3 - Article

AN - SCOPUS:33748773348

VL - 39

SP - 12153

EP - 12165

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 39

M1 - S09

ER -