2022
DOI: 10.48550/arxiv.2202.08723
|View full text |Cite
Preprint
|
Sign up to set email alerts
|

Local exact controllability of the 1D nonlinear Schrödinger equation in the case of Dirichlet boundary conditions

Abstract: We consider the 1D nonlinear Schrödinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent [BL10]. In this paper, we study the case of Dirichlet boundary conditions. To establish the controllability of the linearised equation, we use a bilinear control acting through four directions: three Fourier modes and one generic direction. The Fourier modes are appropriately chosen so th… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2022
2022
2023
2023

Publication Types

Select...
1
1

Relationship

0
2

Authors

Journals

citations
Cited by 2 publications
(2 citation statements)
references
References 16 publications
(22 reference statements)
0
2
0
Order By: Relevance
“…In [5], the authors also proved the local controllability of a nonlinear Schrödinger equation with Neumann boundary conditions. The case of Dirichlet boundary conditions has been treated later by Duca and Nersesyan in [26].…”
Section: Bibliographymentioning
confidence: 99%
“…In [5], the authors also proved the local controllability of a nonlinear Schrödinger equation with Neumann boundary conditions. The case of Dirichlet boundary conditions has been treated later by Duca and Nersesyan in [26].…”
Section: Bibliographymentioning
confidence: 99%
“…Saturation techniques have been introduced by Agrachev and Sarychev [1,2] to study the approximate controllability of 2D Navier-Stokes and Euler systems with additive controls, and extended to the 3D case in [23,24]. Other recent developments of these techniques are given, e.g., in [13] to study small-time controllability properties of semiclassical Schr ödinger equations, and in [15] to study local exact controllability of 1D Schr ödinger equations with Dirichlet boundary conditions.…”
Section: Small-time Approximate Controllabilitymentioning
confidence: 99%