On the Cauchy problem for a Kadomtsev-Petviashvili hierarchy on non-formal operators and its relation with a group of diffeomorphisms - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Dynamics of Partial Differential Equations Année : 2024

On the Cauchy problem for a Kadomtsev-Petviashvili hierarchy on non-formal operators and its relation with a group of diffeomorphisms

Résumé

We establish a rigorous link between infinite-dimensional regular Fr\"olicher Lie groups built out of non-formal pseudodifferential operators and the Kadomtsev-Petviashvili hierarchy. We introduce a version of the Kadomtsev-Petviashvili hierarchy on a regular Fr\"olicher Lie group of series of non-formal odd-class pseudodifferential operators. We solve its corresponding Cauchy problem, and we establish a link between the dressing operator for our hierarchy and the action of diffeomorphisms and non-formal Sato-like operators on jet spaces. In appendix, we describe the group of Fourier integral operators in which this correspondence seems to take place. Also, motivated by Mulase's work on the KP hierarchy, we prove a group factorization theorem for our group of Fourier integral operators.
Fichier principal
Vignette du fichier
DiffKP12.pdf (446.75 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01857150 , version 1 (14-08-2018)
hal-01857150 , version 2 (25-05-2020)

Identifiants

Citer

Jean-Pierre Magnot, Enrique G Reyes. On the Cauchy problem for a Kadomtsev-Petviashvili hierarchy on non-formal operators and its relation with a group of diffeomorphisms. Dynamics of Partial Differential Equations, 2024, 21 (3), pp.235-260. ⟨10.4310/DPDE.2024.v21.n3.a2⟩. ⟨hal-01857150v2⟩
82 Consultations
63 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More