On an exact WKB approach to Ablowitz-Segur's connection problem for the second Painlevé equation

Yoshitsugu Takei
2002 ANZIAM journal (Print)  
We discuss Ablowitz-Segur's connection problem for the second Painleve equation from the viewpoint of WKB analysis of Painleve transcendents with a large parameter. The formula they first discovered is rederived from a suitable combination of connection formulas for the first Painleve equation. d 2 k/dt 2 = r) 2 Fj(X, t) + Gj (A, dX/dt, t) ( 7 = 1 , . . . , VI), (/>,)
doi:10.1017/s1446181100007963 fatcat:xwdfqcj775av7lhjg3s3labjl4