The Benjamin-Ono Hierarchy with Asymptotically Reflectionless Initial Data in the Zero-Dispersion Limit

Details The Benjamin-Ono Hierarchy with Asymptotically Reflectionless Initial Data in the Zero-Dispersion Limit The Benjamin-Ono Hierarchy with Asymptotically Reflectionless Initial Data in the Zero-Dispersion Limit

2011-01-04

arxiv.org/abs/1101.0784v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, 2 figures. Submitted to Comm. Math. Sci. special issue in honor of C. D. Levermore's 60th birthday

Scientific paper

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.

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