On multichannel solutions of nonlinear Schr\"{o}dinger equations: algorithm, analysis and numerical explorations
High Energy Physics - Theory
2015-06-19 v2 Quantum Gases
Soft Condensed Matter
Mathematical Physics
math.MP
Abstract
We apply the method of modulation equations to numerically solve the NLS with multichannel dynamics, given by a trapped localized state and radiation. This approach employs the modulation theory of Soffer-Weinstein, which gives a system of ODE's coupled to the radiation term, which is valid for all times. We comment on the differences of this method from the well-known method of collective coordinates.
Cite
@article{arxiv.1404.1159,
title = {On multichannel solutions of nonlinear Schr\"{o}dinger equations: algorithm, analysis and numerical explorations},
author = {Avy Soffer and Xiaofei Zhao},
journal= {arXiv preprint arXiv:1404.1159},
year = {2015}
}
Comments
16 pages, 9 figures. Added a comparison to collective coordinates scheme that includes a radiation term