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This paper has been published in Studies in Applied Mathematics. To download a preprint of this paper just click here.

This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-1206131 and DMS-1513054. Any opinions, findings and conclusions or recomendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

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Direct Scattering for the Benjamin-Ono Equation with Rational Initial Data

Peter D. Miller and Alfredo N. Wetzel

Department of Mathematics, University of Michigan, Ann Arbor


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.