Bäcklund Charts & Applications

Bäcklund transformations are here considered as a tool to investigate nonlinear evolution equations as well as linear ones in the case when a memory term, nonlocal in the time variable, is present. Indeed, the important role played by Bäcklund transformations both in looking for solutions to initial boundary value problems, on one side, and in revealing structural properties, on the other one, are well known. Here, Bäcklund Transformations under the latter viewpoint are applied with the aim to generalize Bäcklund Charts to connect hierarchies of operator valued equations in a suitable Banach Space related to the equations of interest. Further new perspectives as well as results are also mentioned.