Baecklund Charts: commutative versus non-commutative Equation Hierarchies

si veda sopra

Here di↵erent B¨acklund Charts are considered both in the case of Commutative Equation Hierarchies as well as in the case of their Non-Commutative analogues. The aim is to point out di↵erences and analogies[1]. Specifically, the case of the Cole-Hopf link between Burgers and Heat Equations [2, 3] and its extension to the corresponding Hierarchies are considered [4]. Furthermore, links connecting third order nonlinear evolution equations, such as KdV, mKdV are analyzed, again, in both the commutative [5] and noncommutative case [6].