Contents Online
Communications in Mathematical Sciences
Volume 10 (2012)
Number 1
Special Issue on the Occasion of C. David Levermore’s Sixtieth Birthday
The Benjamin-Ono hierarchy with asymptotically reflectionless initial data in the zero-dispersion limit
Pages: 117 – 130
DOI: https://dx.doi.org/10.4310/CMS.2012.v10.n1.a6
Authors
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 infnite family of simultaneously conserved densities in terms of alternating sums of branches of solutions of the inviscid Burgers hierarchy.
Keywords
internal waves, Benjamin-Ono equation, integrable hierarchies, dispersionless asymptotics
2010 Mathematics Subject Classification
35Q35, 35Q53, 37K10, 37K40
Published 14 October 2011