Nonlinear bound states with prescribed angular momentum

We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schrödinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of a non-radially symmetric spatial profile which in itself is ob...

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Published inCalculus of variations and partial differential equations Vol. 63; no. 1; p. 1
Main Authors Nenciu, Irina, Shen, Xiaoan, Sparber, Christof
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2024
Springer Nature B.V
Subjects
Analysis
Angular momentum
Calculus of Variations and Optimal Control; Optimization
Conservation laws
Constraints
Control
Lagrange multiplier
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Schrodinger equation
Systems Theory
Theoretical
35B07
35B35
35Q41
Online AccessGet full text
ISSN0944-2669
1432-0835
DOI10.1007/s00526-023-02599-z

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Summary:We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schrödinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of a non-radially symmetric spatial profile which in itself is obtained via a doubly constrained energy minimization. One of the two constraints imposed is the total mass, while the other is given by the expectation value of the angular momentum around the z -axis. Our approach also allows for a new description of the set of minimizers subject to only a single mass constraint.
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ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02599-z