Dynamics of the Schrödinger–Langevin equation. (18th February 2021)

• Record Type: Journal Article
• Authors: Chauleur, Quentin
• Is Part Of: Nonlinearity. Volume 34:Number 4(2021)
• Page Start: 1943
• Page End: 1974
• Publication Date: 2021-02-18
• Subjects: nonlinear Schrödinger equation -- quantum fluid dynamics -- logarithmic nonlinearity -- global attractor; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/abd528
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider the nonlinear Schrödinger–Langevin equation for both signs of the logarithmic nonlinearity. We explicitly compute the dynamics of Gaussian solutions for large times, which is obtained through the study of a particular nonlinear differential equation of order 2. We then give the asymptotic behavior of general energy weak solutions under some regularity assumptions. Some numerical simulations are performed in order to corroborate the theoretical results.