Multiple Higher-Order Pole Solutions in Spinor Bose–Einstein Condensates

IF 2.6 2区 数学 Q1 MATHEMATICS, APPLIED
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引用次数: 0

Abstract

In this study, multiple higher-order pole solutions of spinor Bose–Einstein condensates are explored by means of the inverse scattering transform, which are associated with different higher-order pole pairs of the transmission coefficient and give solutions to the spin-1 Gross–Pitaevskii equation. First, a direct scattering problem is introduced to map the initial data to the scattering data, which includes discrete spectrums, reflection coefficients, and a polynomial that replaces the normalized constants. In order to analyze symmetries and discrete spectra in the direct scattering problem, a generalized cross product is defined in four-dimensional vector Space. The inverse scattering problem is then characterized in terms of the \(4\times 4\) matrix Riemann–Hilbert problem that is subject to the residual conditions of these higher-order poles. In the reflectionless case, the Riemann–Hilbert problem can be converted into a linear algebraic system, which has a unique solution and allows us to explicitly obtain multiple higher-order pole solutions to the spin-1 Gross–Pitaevskii equation.

旋子玻色-爱因斯坦凝聚态中的多重高阶极解
摘要 本研究通过反散射变换探讨了自旋玻色-爱因斯坦凝聚体的多个高阶极点解,这些解与透射系数的不同高阶极点对相关联,并给出了自旋-1 格罗斯-皮塔耶夫斯基方程的解。首先,引入直接散射问题,将初始数据映射到散射数据,其中包括离散谱、反射系数和替代归一化常数的多项式。为了分析直接散射问题中的对称性和离散光谱,在四维向量空间中定义了广义交叉积。然后,反向散射问题用 \(4\times 4\) 矩阵黎曼-希尔伯特问题来描述,该问题受制于这些高阶极点的残差条件。在无反射情况下,黎曼-希尔伯特问题可以转换成一个线性代数系统,它有一个唯一的解,并允许我们明确地得到自旋-1 格罗斯-皮塔耶夫斯基方程的多个高阶极点解。
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来源期刊
CiteScore
5.00
自引率
3.30%
发文量
87
审稿时长
4.5 months
期刊介绍: The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.
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