Existence and stability of standing waves for nonlinear Schrödinger equations with a critical rotational speed

We study the existence and stability of standing waves associated to the Cauchy problem for the nonlinear Schrödinger equation (NLS) with a critical rotational speed and an axially symmetric harmonic potential. This equation arises as an effective model describing the attractive Bose-Einstein conden...

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Bibliographic Details
Published inLetters in mathematical physics Vol. 112; no. 53
Main Author Dinh, van Duong
Format Journal Article
LanguageEnglish
Published Springer Verlag 05.06.2022
Subjects
Analysis of PDEs
Mathematics
Standing waves
2010 Mathematics Subject Classification. 35A01
Stability
35Q55 Nonlinear Schrödinger equation
Rotation
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ISSN0377-9017
1573-0530

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Summary:We study the existence and stability of standing waves associated to the Cauchy problem for the nonlinear Schrödinger equation (NLS) with a critical rotational speed and an axially symmetric harmonic potential. This equation arises as an effective model describing the attractive Bose-Einstein condensation in a magnetic trap rotating with an angular velocity. By viewing the equation as NLS with a constant magnetic field and with (or without) a partial harmonic confinement, we establish the existence and orbital stability of prescribed mass standing waves for the equation with masssubcritical, mass-critical, and mass-supercritical nonlinearities. Our result extends a recent work of [Bellazzini-Boussaïd-Jeanjean-Visciglia, Comm. Math. Phys. 353 (2017), no. 1, 229-251], where the existence and stability of standing waves for the supercritical NLS with a partial confinement were established.
ISSN:0377-9017
1573-0530