New perspectives for generalized Kadomtsev-Petviashvili hierarchies

In the setting of diffeological differential algebras, we first expose step by step how the classical algebraic construction of the solution of the (classical) Kadomtsev-Petviashvili hierarchy can be extended in order to get well-posedness for Kadomtsev-Petviashvili hierarchies in this generalized setting. Of course, we give a short exposition of the necessary notions in diffeologies for non-specialists of this topic.
Then, we discuss the Hamiltonian formulation in a refreshed way. Finally, we deduce the corresponding Kadomtsev-Petviashvili equations, first in an abstract formulation, and in a series of examples.
References:
arXiv:1007.3543
https://dx.doi.org/10.1080/14029251.2017.1418057
arXiv:1608.03994
arXiv:2101.04523, Mi tmf10046
arXiv:2203.07062
arXiv:2212.07583