• Corpus ID: 119275130

On the tritronquée solutions of P$_I^2$

@article{Kapaev2013OnTT,
  title={On the tritronqu{\'e}e solutions of P\$\_I^2\$},
  author={Andrei A. Kapaev and Christian Klein and Tamara Grava},
  journal={arXiv: Mathematical Physics},
  year={2013}
}
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 $u^{(m)}(x,t)$, $\hat u^{(m)}(x,t)$, $m=0,...,6$, called {\em tritronqu\'ee}, describe the quasi-linear Stokes phenomenon and find the large $n$ asymptotics of the coefficients in a formal… 

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