Abstract
The main aim of this chapter is to explain direct and natural rigorous methods for carrying out local and some global asymptotic studies near fixed singular points of the classical Painlevé equations. Such methods were first developed by Boutroux (around 1913). Here we review these methods and improve Boutroux’s results. Moreover, we show that these methods can also be used to obtain asymptotic behavior in other limits, e.g., when a parameter of the equation becomes large. The methods and results are illustrated here for the first and second Painlevé equations.
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Joshi, N. (1999). Asymptotic Studies of the Painlevé Equations. In: Conte, R. (eds) The Painlevé Property. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1532-5_4
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DOI: https://doi.org/10.1007/978-1-4612-1532-5_4
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