Ground states of the two-dimensional dispersion managed nonlinear Schr\"odinger equation
Analysis of PDEs
2024-09-30 v2
Abstract
We consider the variational problem with a mass constraint arising from the two-dimensional dispersion managed nonlinear Schr\"odinger equation with power-law type nonlinearity. We prove a threshold phenomenon with respect to mass for the existence of minimizers for all possible powers of nonlinearities, including at the threshold itself. This threshold is closely related to the best constant for the Gagliardo-Nirenberg-Strichartz type inequality whose extremizers are found as a byproduct.
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Cite
@article{arxiv.2409.14686,
title = {Ground states of the two-dimensional dispersion managed nonlinear Schr\"odinger equation},
author = {Mi-Ran Choi and Young-Ran Lee},
journal= {arXiv preprint arXiv:2409.14686},
year = {2024}
}
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21 pages