ON (t 2 , t 3 )−ZAKHAROV-SHABAT EQUATIONS OF GENERALIZED KADOMTSEV-PETVIASHVILI HIERARCHIES - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Physics Année : 2022

ON (t 2 , t 3 )−ZAKHAROV-SHABAT EQUATIONS OF GENERALIZED KADOMTSEV-PETVIASHVILI HIERARCHIES

Enrique Reyes
Vladimir Rubtsov
  • Fonction : Auteur
  • PersonId : 1058280

Résumé

We review the integration of the KP hierarchy in several nonstandard contexts. Specifically, we consider KP in the following associative differential algebras: an algebra equipped with a nilpotent derivation; an algebra of functions equipped with a derivation that generalizes the gradient operator; an algebra of quaternion-valued functions; a differential Lie algebra; an algebra of polynomials equipped with the Pincherle differential; a Moyal algebra. In all these cases we can formulate and solve the Cauchy problem of the KP hierarchy. Also, in each of these cases we derive different Zakharov-Shabat (t 2 , t 3)-equations-that is, different Kadomtsev-Petviashvili equations-and we prove existence of solutions arising from solutions to the corresponding KP hierarchy.
Fichier principal
Vignette du fichier
Generalized-KP-v12.pdf (354.22 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03606717 , version 1 (12-03-2022)

Identifiants

Citer

Jean-Pierre Magnot, Enrique Reyes, Vladimir Rubtsov. ON (t 2 , t 3 )−ZAKHAROV-SHABAT EQUATIONS OF GENERALIZED KADOMTSEV-PETVIASHVILI HIERARCHIES. Journal of Mathematical Physics, 2022, 63, pp.093501. ⟨10.1063/5.0093238⟩. ⟨hal-03606717⟩
24 Consultations
22 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More