Sandra Carillo, Mauro Lo Schiavo, Cornelia Schiebold, “Bäcklund Transformations and Non-Abelian Nonlinear Evolution Equations: a Novel Bäcklund Chart”, SIGMA, 2016, Volume 12,087, 17 pp.

This article is cited in 10 papers

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

Sandra Carillo^ab, Mauro Lo Schiavo^b, Cornelia Schiebold^cd

^a I.N.F.N. - Sez. Roma1, Gr. IV - Mathematical Methods in NonLinear Physics, Rome, Italy
^b Dipartimento “Scienze di Base e Applicate per l’Ingegneria”, Sapienza - Università di Roma, 16, Via A. Scarpa, 00161 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

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.

Received: December 8, 2015; in final form August 24, 2016; Published online August 30, 2016

Language: English

DOI: 10.3842/SIGMA.2016.087