Frank, Rupert L.; Méhats, Florian; Sparber, Christof Averaging of nonlinear Schrödinger equations with strong magnetic confinement. (English) Zbl 1387.35549 Commun. Math. Sci. 15, No. 7, 1933-1945 (2017). Summary: We consider the dynamics of nonlinear Schrödinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement, based on the spectral properties of the Landau Hamiltonian. Using an averaging technique we derive an associated effective description via an averaged model of nonlinear Schrödinger type. In a special case, this also yields a derivation of the LLL equation. Cited in 1 ReviewCited in 4 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35B25 Singular perturbations in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 35Q40 PDEs in connection with quantum mechanics 35R09 Integro-partial differential equations Keywords:nonlinear Schrödinger equation; magnetic confinement; Landau levels; averaging PDFBibTeX XMLCite \textit{R. L. Frank} et al., Commun. Math. Sci. 15, No. 7, 1933--1945 (2017; Zbl 1387.35549) Full Text: DOI arXiv