|
This article is cited in 11 scientific papers (total in 11 papers)
Geometric Theory of the Recursion Operators for the Generalized Zakharov–Shabat System in Pole Gauge on the Algebra $\mathrm{sl}(n,\mathbb C)$ with and without Reductions
Alexandar B. Yanovskia, Gaetano Vilasib a Department of Mathematics & Applied Mathematics, University of Cape Town, Rondebosch 7700, Cape Town, South Africa
b Dipartimento di Fisica, Universitè degli Studi di Salerno, INFN, Sezione di Napoli-GC Salerno, Via Ponte Don Melillo, 84084, Fisciano (Salerno), Italy
Abstract:
We consider the recursion operator approach to the soliton equations related to the generalized Zakharov–Shabat system on the algebra $\mathrm{sl}(n,\mathbb C)$ 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.
Keywords:
Lax representation; recursion operators; Nijenhuis tensors.
Received: May 17, 2012; in final form November 5, 2012; Published online November 16, 2012
Citation:
Alexandar B. Yanovski, Gaetano Vilasi, “Geometric Theory of the Recursion Operators for the Generalized Zakharov–Shabat System in Pole Gauge on the Algebra $\mathrm{sl}(n,\mathbb C)$ with and without Reductions”, SIGMA, 8 (2012), 087, 23 pp.
Linking options:
https://www.mathnet.ru/eng/sigma764 https://www.mathnet.ru/eng/sigma/v8/p87
|
Statistics & downloads: |
Abstract page: | 239 | Full-text PDF : | 37 | References: | 70 |
|