### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 087, 17 pages      arXiv:1512.02386      https://doi.org/10.3842/SIGMA.2016.087
Contribution to the Special Issue on Analytical Mechanics and Differential Geometry in honour of Sergio Benenti

### Bäcklund Transformations and Non-Abelian Nonlinear Evolution Equations: a Novel Bäcklund Chart

Sandra Carillo ab, Mauro Lo Schiavo a and Cornelia Schiebold cd
a) Dipartimento ''Scienze di Base e Applicate per l'Ingegneria'', Sapienza - Università di Roma, 16, Via A. Scarpa, 00161 Rome, Italy
b) I.N.F.N. - Sez. Roma1, Gr. IV - Mathematical Methods in NonLinear Physics, Rome, Italy
c) Department of Science Education and Mathematics, Mid Sweden University, S-851 70 Sundsvall, Sweden
d) Instytut Matematyki, Uniwersytet Jana Kochanowskiego w Kielcach, Poland

Received December 08, 2015, in final form August 24, 2016; Published online August 30, 2016

Abstract
Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative Bäcklund chart, generalizing results in [Fuchssteiner B., Carillo S., Phys. A 154 (1989), 467-510]. The recursion operators are shown to be hereditary, thereby allowing the results to be extended to hierarchies. The present study is devoted to operator nonlinear evolution equations: general results are presented. The implied applications referring to finite-dimensional cases will be considered separately.

Key words: .

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