The Benjamin-Ono Hierarchy with Asymptotically Reflectionless Initial Data in the Zero-Dispersion Limit
Exactly Solvable and Integrable Systems
2015-03-17 v1 Analysis of PDEs
Abstract
We study the Benjamin-Ono hierarchy with positive initial data of a general type, in the limit when the dispersion parameter tends to zero. We establish simple formulae for the limits (in appropriate weak or distributional senses) of an infinite family of simultaneously conserved densities in terms of alternating sums of branches of solutions of the inviscid Burgers hierarchy.
Cite
@article{arxiv.1101.0784,
title = {The Benjamin-Ono Hierarchy with Asymptotically Reflectionless Initial Data in the Zero-Dispersion Limit},
author = {Peter D. Miller and Zhengjie Xu},
journal= {arXiv preprint arXiv:1101.0784},
year = {2015}
}
Comments
12 pages, 2 figures. Submitted to Comm. Math. Sci. special issue in honor of C. D. Levermore's 60th birthday