Open Access
2010 On Generalized Fourier Transform for Kaup-Kupershmidt Type Equations
Tihomir Valchev
J. Geom. Symmetry Phys. 19: 73-86 (2010). DOI: 10.7546/jgsp-19-2010-73-86


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.


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Tihomir Valchev. "On Generalized Fourier Transform for Kaup-Kupershmidt Type Equations." J. Geom. Symmetry Phys. 19 73 - 86, 2010.


Published: 2010
First available in Project Euclid: 25 May 2017

zbMATH: 1203.37113
MathSciNet: MR2674962
Digital Object Identifier: 10.7546/jgsp-19-2010-73-86

Rights: Copyright © 2010 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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