Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl( n ,C)

[摘要] We consider the recursion operator approach to the soliton equations related to the generalized Zakharov-Shabat system on the algebra sl( n , C ) in pole gauge both in the general position and in the presence of reductions. We present the recursion operators and discuss their geometric meaning as conjugate to Nijenhuis tensors for a Poisson-Nijenhuis structure defined on the manifold of potentials.

[关键词] Lax representation;recursion operators;Nijenhuis tensors