For equation , the second member in the PI hierarchy, we prove existence of various degenerate solutions depending on the complex parameter and evaluate the asymptotics in the complex plane for and . Using this result, we identify the most degenerate solutions , , , called tritronqu,e; describe the quasi-linear Stokes phenomenon; and find the large asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronqu,e solutions.
