Standing waves for the nonlinear Schrödinger equation coupled with the Maxwell equation

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 th...

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Bibliographic Details
Published in:Nonlinearity 2017-05, Vol.30 (5), p.1920-1947
Main Authors: Colin, Mathieu, Watanabe, Tatsuya
Format: Article
Language:English
Subjects:
Analysis of PDEs
constraint minimization problem
ground states
Mathematics
orbital stability of standing waves
Schrödinger-Maxwell system
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Summary: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.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa6760