106 citations · 106 across the 1 of their papers we have counts for
7 papers
Degasperis-Procesi peakons and the discrete cubic string
Hans Lundmark, Jacek Szmigielski
We use an inverse scattering approach to study multi-peakon solutions of the Degasperis-Procesi (DP) equation, an integrable PDE similar to the Camassa-Holm shallow water equation.…
Vertex operator algebras and the representation theory of toroidal algebras
S. Berman, Y. Billig, J. Szmigielski
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
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…
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…
Representations of the Heisenberg algebra by difference operators
Andrzej Z. Gorski, Jacek Szmigielski
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence princ…
Principal Realization for the extended affine Lie algebra of type with coordinates in a simple quantum torus with two generators
Stephen Berman, Jacek Szmigielski
We construct an irreducible representation for the extended affine algebra of type with coordinates in a quantum torus. We explicitly give formulas using vertex operators si…