Valchev, Tihomir On generalized Fourier transform for Kaup-Kupershmidt type equations. (English) Zbl 1203.37113 J. Geom. Symmetry Phys. 19, 73-86 (2010). Summary: 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. Cited in 1 ReviewCited in 2 Documents MSC: 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35Q53 KdV equations (Korteweg-de Vries equations) 37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems 37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures Keywords:inverse scattering method; Fourier transform; Zakharov-Shabat system; Lie algebra; Kaup-Kupershmidt equation PDF BibTeX XML Cite \textit{T. Valchev}, J. Geom. Symmetry Phys. 19, 73--86 (2010; Zbl 1203.37113)