Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data
Exactly Solvable and Integrable Systems
2015-04-29 v1 Analysis of PDEs
Classical Analysis and ODEs
Complex Variables
Spectral Theory
Abstract
We compute the scattering data of the Benjamin-Ono equation for arbitrary rational initial conditions with simple poles. Specifically, we obtain explicit formulas for the Jost solutions and eigenfunctions of the associated spectral problem, yielding an Evans function for the eigenvalues and formulas for the phase constants and reflection coefficient.
Cite
@article{arxiv.1504.07610,
title = {Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data},
author = {Peter D. Miller and Alfredo N. Wetzel},
journal= {arXiv preprint arXiv:1504.07610},
year = {2015}
}
Comments
16 Pages, 2 Figures