Alexandar B. Yanovski, Gaetano Vilasi, “Geometric Theory of the Recursion Operators for the Generalized Zakharov–Shabat System in Pole Gauge on the Algebra <nobr>$\mathrm{sl}(n,\mathbb C)$</nobr> with and without Reductions”, SIGMA, 2012, Volume 8,087, 23 pp.

This article is cited 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. Yanovski^a, Gaetano Vilasi^b

^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.

MSC: 35Q51; 37K05; 37K10

Received: May 17, 2012; in final form November 5, 2012; Published online November 16, 2012

Language: English

DOI: 10.3842/SIGMA.2012.087