Multiple higher-order poles solutions in spinor Bose-Einstein condensates
Abstract
In this study, we explore multiple higher-order pole solutions in spinor Bose--Einstein condensates. These solutions are associated with different pairs of higher-order poles of the transmission coefficient in the inverse scattering transform, and they represent solutions of the spin-1 Gross--Pitaevskii equation. We introduce a direct scattering map that maps initial data to scattering data, which includes discrete spectrums, reflection coefficients, and a polynomial that replaces normalization constants. To analyze symmetries and discrete spectrums in the direct problem, we introduce a generalized cross product in 4-dimensional vector space. Additionally, we characterize the inverse problem in terms of a matrix Riemann--Hilbert problem that is subject to residue conditions at these higher-order poles. In the reflectionless scenario, the Riemann--Hilbert problem can be converted into a linear algebraic system. The resulting algebraic system has a unique solution, which allows us to display multiple higher-order poles solutions.
Keywords
Cite
@article{arxiv.2402.08362,
title = {Multiple higher-order poles solutions in spinor Bose-Einstein condensates},
author = {Huan Liu and Jing Shen and Xianguo Geng},
journal= {arXiv preprint arXiv:2402.08362},
year = {2024}
}