Conserved energies for the one dimensional Gross-Pitaevskii equation
Analysis of PDEs
2019-07-30 v2
Abstract
We prove the global-in-time well-posedness of the one dimensional Gross-Pitaevskii equation in the energy space, which is a complete metric space equipped with a newly introduced metric and with the energy norm describing the regularities of the solutions. We establish a family of conserved energies for the one dimensional Gross-Pitaevskii equation, such that the energy norms of the solutions are conserved globally in time. This family of energies is also conserved by the complex modified Korteweg-de Vries flow.
Keywords
Cite
@article{arxiv.1801.08386,
title = {Conserved energies for the one dimensional Gross-Pitaevskii equation},
author = {Herbert Koch and Xian Liao},
journal= {arXiv preprint arXiv:1801.08386},
year = {2019}
}