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Connection formulae for asymptotics of the fifth Painlevé transcendent on the imaginary axis: I
Studies in Applied Mathematics ( IF 2.7 ) Pub Date : 2020-07-02 , DOI: 10.1111/sapm.12323
Fedor V. Andreev 1 , Alexander V. Kitaev 2
Affiliation  

Leading terms of asymptotic expansions for the general complex solutions of the fifth Painleve equation as $t\to\imath\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$ \frac{d}{d\lambda}Y= \left(\frac t2\sigma_3 + \frac{A_0}\lambda+\frac{A_1}{\lambda-1}\right)Y. $$ The parametrization allows one to derive connection formulas for the asymptotics. We provide numerical verification of the results. Important special cases of the connection formulas are also considered.

中文翻译:

虚轴上第五个 Painlevé 超越的渐近线的连接公式:I

找到了作为 $t\to\imath\infty$ 的第五 Painleve 方程的一般复解的渐近展开式的主要项。这些渐近线由相关线性常微分方程的单项数据参数化。$$ \frac{d}{d\lambda}Y= \left(\frac t2\sigma_3 + \frac{A_0}\lambda+\frac{A_1}{\lambda-1}\right)Y。$$ 参数化允许推导出渐近线的连接公式。我们提供结果的数值验证。还考虑了连接公式的重要特殊情况。
更新日期:2020-07-02
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