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

Sandra Carillo ; Mauro Lo Schiavo ; Cornelia Schiebold

Symmetry, integrability and geometry: methods and applications, Tome 12 (2016)

Résumé

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.

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