Statistical mechanics of the periodic Benjamin Ono equation

Blower, Gordon and Brett, Caroline and Doust, Ian (2019) Statistical mechanics of the periodic Benjamin Ono equation. Journal of Mathematical Physics, 60 (9): 093302. ISSN 0022-2488

[thumbnail of BONOSU~1]
Text (BONOSU~1)
BONOSU_1.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (485kB)


The periodic Benjamin--Ono equation is an autonomous Hamiltonian system with a Gibbs measure on $L^2({\mathbb T})$. The paper shows that the Gibbs measures on bounded balls of $L^2$ satisfy some logarithmic Sobolev inequalities. The space of $n$-soliton solutions of the periodic Benjamin--Ono equation, as discovered by Case, is a Hamiltonian system with an invariant Gibbs measure. As $n\rightarrow\infty$, these Gibbs measures exhibit a concentration of measure phenomenon. Case introduced soliton solutions that are parameterised by atomic measures in the complex plane. The limiting distributions of these measures gives the density of a compressible gas that satisfies the isentropic Euler equations.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Mathematical Physics
Additional Information:
Copyright 2019 American Institute of Physics. The following article appeared in Journal of Mathematical Physics 60, 2019 and may be found at This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Uncontrolled Keywords:
?? statistical mechanicslogarithmic sobolev inequalitysolitonsmathematics(all)mathematical physicsstatistical and nonlinear physics ??
ID Code:
Deposited By:
Deposited On:
23 Sep 2019 14:45
Last Modified:
18 Apr 2024 00:45