Nonlinear bound states with prescribed angular momentum
Abstract
We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schr\"odinger 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.
Cite
@article{arxiv.2303.02236,
title = {Nonlinear bound states with prescribed angular momentum},
author = {Irina Nenciu and Xiaoan Shen and Christof Sparber},
journal= {arXiv preprint arXiv:2303.02236},
year = {2024}
}
Comments
17 pages; more discussion regarding the regularity and irregularity of the doubly constrained set added (see lemma 2.6 and proposition 2.7)