ON THE CAUCHY PROBLEM FOR A DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION WITH NONVANISHING BOUNDARY CONDITIONS - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Evolution Equations and Control Theory (EECT) Année : 2021

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.
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Dates et versions

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

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Phan van Tin. ON THE CAUCHY PROBLEM FOR A DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION WITH NONVANISHING BOUNDARY CONDITIONS. Evolution Equations and Control Theory (EECT), 2021, ⟨10.3934/eect.2021028⟩. ⟨hal-03083232v3⟩
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