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Application of uniform asymptotics to the fifth Painlevé transcendent. (English) Zbl 1010.34082

The authors study the general fifth Painlevé equation and apply the uniform asymptotic method to the fifth Painlevé transcendents. Further, they find its asymptotics of the form \(y=-1+t^{-1/2} A(t)\) as \(t\to \infty\) along the positive \(t\)-axis and obtain the corresponding monodromy data.

MSC:

34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
34E05 Asymptotic expansions of solutions to ordinary differential equations
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