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VOL. 9 | 2008 On the Kaup-Kupershmidt Equation: On the Polarization of Gravitational Waves

Abstract

We regard a cubic spectral problem associated with the Kaup-Kupershmidt equation. For this spectral problem we prove a completeness of its “squared” solutions and derive the completeness relations which they satisfy. The spectral problem under consideration can be naturally viewed as a $\mathbb{Z}_{3}$-reduced Zakharov-Shabat problem related to the algebra $\mathfrak{sl}(3,\mathbb{C})$. This observation is crucial for our considerations.

Information

Published: 1 January 2008
First available in Project Euclid: 13 July 2015

zbMATH: 1193.35200
MathSciNet: MR2436282

Digital Object Identifier: 10.7546/giq-9-2008-308-319

Rights: Copyright © 2008 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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