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- Title
Multiple Higher-Order Pole Solutions in Spinor Bose–Einstein Condensates.
- Authors
Liu, Huan; Shen, Jing; Geng, Xianguo
- 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 × 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.
- Publication
Journal of Nonlinear Science, 2024, Vol 34, Issue 3, p1
- ISSN
0938-8974
- Publication type
Article
- DOI
10.1007/s00332-024-10024-8