Yanovski, Alexander B. Geometric interpretation of the recursion operators for the generalized Zakharov-Shabat system in pole gauge on the Lie algebra \(A_2\). (English) Zbl 1235.35238 J. Geom. Symmetry Phys. 23, 97-111 (2011). Summary: We consider the recursion operator approach to the soliton equations related to a generalized Zakharov-Shabat auxiliary linear system in pole gauge on the Lie algebra \(A_2=\mathfrak{sl}(3,\mathbb{C})\) and show that the recursion operator can be identified with the dual to a Nijenhuis tensor for a Poisson-Nijenhuis structure on the manifold of potentials. Cited in 4 Documents MSC: 35Q51 Soliton equations 37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems 35C08 Soliton solutions 17B81 Applications of Lie (super)algebras to physics, etc. Keywords:soliton equations; Zakharov-Shabat system; Lie algebra; Poisson-Nijenhuis structure × Cite Format Result Cite Review PDF