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A novel noncommutative KdV-type equation, its recursion operator, and solitons

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Author list: Porten, Egmont;Schiebold, Cornelia

Publication year: 2018

ISSN: 0022-2488

DOI: http://dx.doi.org/10.1063/1.5027481


Abstract

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.


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