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

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.

References in corpus (3)

• With a Cole-Hopf transformation to solutions of the noncommutative KP hierarchy in terms of Wronski matrices
• Recursion Operators admitted by non-Abelian Burgers equations: Some Remarks
• Multicomponent Burgers and KP Hierarchies, and Solutions from a Matrix Linear System

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• Soliton Scattering in Noncommutative Spaces
• Ermakov-Pinney and Emden-Fowler equations: new solutions from novel Bäcklund transformations
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• Bäcklund transformations: a tool to study Abelian and non-Abelian nonlinear evolution equations