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

Symmetry Integrability and Geometry-Methods and Applications

article

Alexandar B. Yanovski¹  Gaetano Vilasi² 

[1] Department of Mathematics & Applied Mathematics, University of Cape Town;Dipartimento di Fisica, Università degli Studi di Salerno

关键词: Lax representation;    recursion operators;    Nijenhuis tensors;   

DOI  :  10.3842/SIGMA.2012.087

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown