ON THE CAUCHY PROBLEM FOR A DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION WITH NONVANISHING BOUNDARY CONDITIONS - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

ON THE CAUCHY PROBLEM FOR A DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION WITH NONVANISHING BOUNDARY CONDITIONS

Résumé

In this paper we consider the Schrödinger equation with nonlinear derivative term. Our goal is to initiate the study of this equation with non vanishing boundary conditions. We obtain the local well posedness for the Cauchy problem on Zhidkov spaces X k (R) and in φ + H k (R). Moreover, we prove the existence of conservation laws by using localizing functions. Finally, we give explicit formulas for stationary solutions on Zhidkov spaces.
Fichier principal
Vignette du fichier
On the derivative Schrodinger equation with nonvanishing boundary conditon new version.pdf (498.82 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03083232 , version 1 (18-12-2020)
hal-03083232 , version 2 (21-01-2021)
hal-03083232 , version 3 (27-09-2021)

Identifiants

  • HAL Id : hal-03083232 , version 1

Citer

Phan van Tin. ON THE CAUCHY PROBLEM FOR A DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION WITH NONVANISHING BOUNDARY CONDITIONS. 2020. ⟨hal-03083232v1⟩
452 Consultations
153 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More