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This paper was originally published in Comm. Math. Sci. To download a preprint of this paper just click here.

This material is based upon work supported by the National Science Foundation under Grant No. DMS-0807653. Any opinions, findings and conclusions or recomendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

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

Peter D. Miller and Zhengjie Xu
Department of Mathematics, University of Michigan, Ann Arbor


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.