Hirota bilinear approach to GUE, NLS, and Painlev\'e IV
Exactly Solvable and Integrable Systems
2015-10-27 v1 Mathematical Physics
math.MP
Abstract
Tracy and Widom showed that the level spacing function of the Gaussian unitary ensemble is related to a particular solution of the fourth Painlev\'e equation. We reconsider this problem from the viewpoint of Hirota's bilinear method in soliton theory and present another proof. We also consider the asymptotic behavior of the level spacing function as , and its relation to the "Clarkson-McLeod solution" to the Painlev\'e IV equation.
Keywords
Cite
@article{arxiv.1510.07560,
title = {Hirota bilinear approach to GUE, NLS, and Painlev\'e IV},
author = {Saburo Kakei},
journal= {arXiv preprint arXiv:1510.07560},
year = {2015}
}
Comments
15 pages