Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Section on Rigorous Nonlinear Analysis
Hirota bilinear approach to GUE, NLS, and Painlevé IV
Saburo Kakei
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2016 Volume 7 Issue 3 Pages 324-337

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Abstract

Tracy and Widom showed that the level spacing function of the Gaussian unitary ensemble is related to a particular solution of the fourth Painlevé 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 s→ ∞, and its relation to the “Clarkson-McLeod solution” to the Painlevé IV equation.

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© 2016 The Institute of Electronics, Information and Communication Engineers
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