Abstract:
This paper proposes a new approach to the asymptotic analysis of Painlevé equations. The approach is based on representing solutions of the Painlevé equations using formal series in two variables, $\sum_{k=0}^{\infty}y^kA_k(x)$, with rational functions $A_k(x)$. The approach is applied to the asymptotic analysis of the third degenerate Painlevé equation.
Key words and phrases:Painlevé property, Painlevé equation, elliptic function, asymptotic series, generating function.
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