Standing waves for the nonlinear Schrödinger equation coupled with the Maxwell equation. (4th April 2017)

• Record Type: Journal Article
• Authors: Colin, Mathieu; Watanabe, Tatsuya
• Is Part Of: Nonlinearity. Volume 30:Number 5(2017:May)
• Page Start: 1920
• Page End: 1947
• Publication Date: 2017-04-04
• Subjects: Schrödinger–Maxwell system -- constraint minimization problem -- ground states -- orbital stability of standing waves; 35J20 -- 35B35 -- 35Q55; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa6760
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we are interested in standing waves of the nonlinear Schrödinger equation coupled with the Maxwell equation. Firstly we describe conditions for the existence of minimizers with prescribed charge in terms of a coupling constant e . Secondly we study the existence of ground states for the stationary problem, the uniqueness of ground states for small e and a link between minimizers and ground states. Finally we study the orbital stability of standing waves for the quadratic nonlinearity.