Abstract
We develop the Fourier transform interpretation of the inverse scattering method for nonlinear integrable evolution equations associated with a $\mathbb{Z}_3$ reduced Zakharov-Shabat system for the Lie algebra $\mathfrak{sl}(3,\mathbb{C})$. A simple representative of this integrable hierarchy is the well-known Kaup-Kupershmidt equation. Our results admit a natural extention for nonlinear equations connected to a deeply reduced Zakharov-Shabat system related to an arbitrary simple Lie algebra.
Information
Published: 1 January 2010
First available in Project Euclid: 13 July 2015
zbMATH: 1203.37113
MathSciNet: MR2757934
Digital Object Identifier: 10.7546/giq-11-2010-198-210
Rights: Copyright © 2010 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
