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SIGMA, 2012, Volume 8, 087, 23 pages (Mi sigma764)  

This article is cited in 8 scientific papers (total in 8 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.


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ArXiv: 1211.3803
Document Type: Article
MSC: 35Q51; 37K05; 37K10
Received: May 17, 2012; in final form November 5, 2012; Published online November 16, 2012
Language: English

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.

Citation in format AMSBIB
\by Alexandar~B.~Yanovski, Gaetano~Vilasi
\paper 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
\jour SIGMA
\yr 2012
\vol 8
\papernumber 087
\totalpages 23

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    This publication is cited in the following articles:
    1. Gerdjikov, V.S., Yanovski, A.B., “On soliton equations with Zh and Dh reductions: Conservation laws and generating operators”, Journal of Geometry and Symmetry in Physics, 31 (2013), 57–92  crossref  mathscinet  zmath  scopus
    2. Gerdjikov V.S. Yanovski A.B., “Cbc Systems With Mikhailov Reductions By Coxeter Automorphism: i. Spectral Theory of the Recursion Operators”, Stud. Appl. Math., 134:2 (2015), 145–180  crossref  mathscinet  zmath  isi  elib  scopus
    3. Gerdjikov V.S., Mladenov D.M., Stefanov A.A., Varbev S.K., “Integrable Equations and Recursion Operators Related To the Affine Lie Algebras a(R)((1))”, J. Math. Phys., 56:5 (2015), 052702  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Gerdjikov, V. S., “On Kaup-Kupershchmidt-type equations and their soliton solutions”, Il Nuovo Cimento C - Colloquia and communications in physics, 38:5 (2015), 161  crossref  scopus
    5. Yanovski, A.; Vilasi, G., “Recursion Operators for CBC system with reductions. Geometric theory”, NUOVO CIMENTO C-COLLOQUIA AND COMMUNICATIONS IN PHYSICS, 38:5 (2015), 172  crossref  scopus
    6. Gerdjikov, V. S.; Mladenov, D. M.; Stefanov, A. A.; Varbev, S. K., “MKdV-type of equations related to $B^{(1)}_2$ and $A^{(2)}_4$”, Springer Proceedings in Physics, 163 (2015), 59-69  crossref  mathscinet  zmath  scopus
    7. Yanovski A.B., Valchev T.I., “Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. i. Auxiliary System and Fundamental Properties”, J. Nonlinear Math. Phys., 25:2 (2018), 324–350  crossref  mathscinet  isi
    8. Yanovski A.B., Valchev T.I., “Hermitian and Pseudo-Hermitian Reduction of the Gmv Auxiliary System. Spectral Properties of the Recursion Operators”, Advanced Computing in Industrial Mathematics (Bgsiam 2017), Studies in Computational Intelligence, 793, eds. Georgiev K., Todorov M., Georgiev I., Springer International Publishing Ag, 2019, 433–446  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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