The Benjamin-Ono Hierarchy with Asymptotically Reflectionless Initial   Data in the Zero-Dispersion Limit
  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. 
Peter D. Miller and Zhengjie Xu
nlin.SI math.AP