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

PHYSICA D-NONLINEAR PHENOMENA

卷:333

Article; Proceedings Paper

Miller, Peter D.¹  Wetzel, Alfredo N.¹ 

[1] Univ Michigan, Dept Math, East Hall,530 Church St, Ann Arbor, MI 48109 USA

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

DOI  :  10.1016/j.physd.2015.07.012

来源: Elsevier

【 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.

【 授权许可】

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