Rational solutions of Painlev\'{e}-II equation as Gram determinant
Exactly Solvable and Integrable Systems
2022-03-08 v1 Mathematical Physics
math.MP
Abstract
Under the Flaschka-Newell Lax pair, the Darboux transformation for the Painlev\'{e}-II equation is constructed by the limiting technique. With the aid of the Darboux transformation, the rational solutions are represented by the Gram determinant, and then we give the large asymptotics of the determinant and the rational solutions. Finally, the solution of the corresponding Riemann-Hilbert problem is obtained from the Darboux matrices.
Keywords
Cite
@article{arxiv.2203.02647,
title = {Rational solutions of Painlev\'{e}-II equation as Gram determinant},
author = {Liming Ling and Bing-Ying Lu and Xiaoen Zhang},
journal= {arXiv preprint arXiv:2203.02647},
year = {2022}
}
Comments
17pages, 1 figure