Resurgent Structure For The First Painlevé Equation
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We show the resurgence property for the formal series solution of the prepared form associated with the first Painlevé equation. The detailed resurgent structure is given in Sect. 8.1. Its proof is given using the so-called bridge equation (Sect. 8.4), after some preliminaries (Sect. 8.3). The nonlinear Stokes phenomena are briefly analyzed in Sect. 8.2.
KeywordsFormal Series Differential Algebra Stokes Phenomenon Exponential Asymptotics Toulouse Math
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