Connection formulas for the Ablowitz-Segur solutions of the inhomogeneous Painlevé II equation

Dan Dai, Weiying Hu

We consider the second Painlevé equation $$u"(x)=2u^3(x)+xu(x)-\alpha ,$$ where $\alpha$ is a nonzero constant. Using the Deift-Zhou nonlinear steepest descent method for Riemann-Hilbert pr…