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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

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.

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.
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