From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Journal of Applied Science and Mathematics Année : 2017

From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters

Résumé

We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N −1 parameters. We construct here N-order rational solutions. We prove that they can be written as a quotient of 2 polynomials of degree 2N(N +1) in x, y and t depending on 2N−2 parameters. We explicitly construct the expressions of the rational solutions of order 4 depending on 6 real parameters and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, b1, b2, b3.
Fichier principal
Vignette du fichier
halKPRAT2NSMMV1.pdf (860.05 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01525384 , version 1 (20-05-2017)
hal-01525384 , version 2 (19-08-2017)

Identifiants

  • HAL Id : hal-01525384 , version 2

Citer

Pierre Gaillard. From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters. International Journal of Applied Science and Mathematics, 2017, 4 (3), pp.60-70. ⟨hal-01525384v2⟩
278 Consultations
113 Téléchargements

Partager

Gmail Facebook X LinkedIn More