On the tritronquée solutions of P$_I^2$
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Grava, Tamara | |
| dc.contributor.author | Kapaev, Andrei | |
| dc.contributor.author | Klein, Christian | |
| dc.date.accessioned | 2014-01-15T07:55:21Z | |
| dc.date.available | 2014-01-15T07:55:21Z | |
| dc.date.issued | 2014-01-15 | |
| dc.description.abstract | 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. | en_US |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/7244 | |
| dc.language.iso | en | en_US |
| dc.miur.area | 1 | en_US |
| dc.publisher | SISSA | en_US |
| dc.subject.miur | MAT/07 FISICA MATEMATICA | |
| dc.title | On the tritronquée solutions of P$_I^2$ | en_US |
| dc.type | Preprint | en_US |