## 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.