Singular asymptotics for solutions of the inhomogeneous Painlevé II equation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)3843-3872
Journal / PublicationNonlinearity
Issue number10
Online published6 Sep 2019
Publication statusPublished - Oct 2019


We consider a family of solutions of the Painlevé II equation
u″(x) = 2u3(x) + xu(x)−α          withα ∈ ℝ \ {0}, 
which has infinitely many poles on (−∞, 0). Using the Deift–Zhou nonlinearsteepest descent method for Riemann–Hilbert problems, we rigorously derivetheir singular asymptotics as x → −∞. In addition, we extend the existingasymptotic results when x → +∞ from α − 12 ∈/ Z to any real α. Theconnection formulas are also obtained.

Research Area(s)

  • Painlevé II equation, singular asymptotics, Riemann-Hilbert problem, connection formulas, DE-VRIES EQUATION, RESPECT, EDGE