Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256329 | Physica D: Nonlinear Phenomena | 2016 | 15 Pages |
Abstract
Using exact formulae for the scattering data of the Benjamin-Ono equation valid for general rational potentials recently obtained in Miller and Wetzel [17], we rigorously analyze the scattering data in the small-dispersion limit. In particular, we deduce precise asymptotic formulae for the reflection coefficient, the location of the eigenvalues and their density, and the asymptotic dependence of the phase constant (associated with each eigenvalue) on the eigenvalue itself. Our results give direct confirmation of conjectures in the literature that have been partly justified by means of inverse scattering, and they also provide new details not previously reported in the literature.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Peter D. Miller, Alfredo N. Wetzel,