302 citations · 1k across the 44 of their papers we have counts for
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Multipeakons and the Classical Moment Problem
Richard Beals, D. H. Sattinger, J. Szmigielski
Classical results of Stieltjes are used to obtain explicit formulas for the peakon-antipeakon solutions of the Camassa-Holm equation. The closed form solution is expressed in terms…
Multipeakons and a theorem of Stieltjes
R. Beals, D. H. Sattinger, J. Szmigielski
A closed form of the multi-peakon solutions of the Camassa-Holm equation is found using a theorem of Stieltjes on continued fractions. An explicit formula is obtained for the scatt…
Acoustic Scattering and the Extended Korteweg deVries hierarchy
R. Beals, D. H. Sattinger, J. Szmigielski
The acoustic scattering operator on the real line is mapped to a Schrödinger operator under the Liouville transformation. The potentials in the image are characterized precisely in…
Factorization and the Dressing Method for the Gel'fand-Dikii Hierarch
D. H. Sattinger, J. S. Szmigielski
The isospectral flows of an order linear scalar differential operator under the hypothesis that it possess a Baker-Akhiezer function were originally investigated by Se…
Systems of PDEs obtained from factorization in loop groups
J. Dorfmeister, H. Gradl, J. Szmigielski
We propose a generalization of a Drinfeld-Sokolov scheme of attaching integrable systems of PDEs to affine Kac-Moody algebras. With every affine Kac-Moody algebra and a parab…
A Riemann-Hilbert Problem for an Energy Dependent Schrödinger Operator
David H. Sattinger, Jacek Szmigielski
\We consider an inverse scattering problem for Schrödinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann s…