Analytic solutions of q-P(A(1)) near its critical points

作者：Joshi Nalini^*; Roffelsen Pieter

来源：Nonlinearity, 2016, 29(12): 3696-3742.

DOI：10.1088/0951-7715/29/12/3696

• q-difference equations
• discrete integrable systems
• Painleve equations
• asymptotics of solutions near critical points
• asymptotic analysis
• Painleve transcendents

For transcendental functions that solve non-linear q-difference equations, the best descriptions available are the ones obtained by expansion near critical points at the origin and infinity. We describe such solutions of a q-discrete Painleve equation, with seven parameters whose initial value space is a rational surface of type A(1)((1)). The resultant expansions are shown to approach series expansions of the classical sixth Painleve equation in the continuum limit.

• 出版日期2016-12