On generalized Fourier transform for Kaup-Kupershmidt type equations
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2010-01-01
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Abstract
We develop the Fourier transform interpretation of the inverse scattering method for nonlinear integrable evolution equations associated with a ℤ3 reduced Zakharov-Shabat system for the Lie algebra sl(3,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.