01011nas a2200133   4500008004100000245004500041210003400086260001000120520062000130100001800750700001900768700002100787856006900808       2013                        en  d00aOn the tritronquée solutions of P$_I^2$0 atritronquée solutions of PI2  bSISSA3 a<p>For equation P$_I^2$, the second member in the P$_I$ hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $t$ and evaluate the asymptotics in the complex $x$ plane for $|x|\to\infty$ and $t=o(x^{2/3})$. Using this result, we identify the most degenerate solutions $u^{(m)}(x,t)$, $\hat u^{(m)}(x,t)$, $m=0,\dots,6$, called {\em tritronqu\'ee}, describe the quasi-linear Stokes phenomenon and find the large $n$ asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronqu\'ee solutions.</p>1 aGrava, Tamara1 aKapaev, Andrey1 aKlein, Christian  uhttps://math.sissa.it/publication/tritronqu%C3%A9e-solutions-pi2