论文标题
（un）扰动的第一个painlevé方程式的指数式渐近渐近渐近差异和数字
Exponentially-improved asymptotics and numerics for the (un)perturbed first Painlevé equation
论文作者
论文摘要
扰动的第一个painlevé方程的解决方案$ y“ = 6y^2-x^μ$，$μ> -4 $，由自由常数$ c $唯一确定，在完整的$ x $ x $ besymptotic扩展中乘以指数的小术语。给出了全面详细信息。全部详细信息，包括非线性的stokes stokes stokes stokes computiers computert computert and computimpt and computert satokations satokeations satokations。根据$ c $的不同，对于这些指数重新提高的渐进式扩展的奇异性的位置，几个数值示例。
The solutions of the perturbed first Painlevé equation $y"=6y^2-x^μ$, $μ>-4$, are uniquely determined by the free constant $C$ multiplying the exponentially small terms in the complete large $x$ asymptotic expansions. Full details are given, including the nonlinear Stokes phenomenon, and the computation of the relevant Stokes multipliers. We derive asymptotic approximations, depending on $C$, for the locations of the singularities that appear on the boundary of the sectors of validity of these exponentially-improved asymptotic expansions. Several numerical examples illustrate the power of the approximations. For the tri-tronquée solution of the unperturbed first Painlevé equation we give highly accurate numerics for the values at the origin and the locations of the zeros and poles.
