The scattering transform for the Benjamin-Ono equation in the small-dispersion limit

[摘要] 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. (C) 2015 Elsevier B.V. All rights reserved.

[发布日期] 2016-10-15

[效力级别]  Proceedings Paper

[关键词] Benjamin-Ono equation;Inverse-scattering transform;Small-dispersion limit