We study solitons of general topological charge over noncommutative tori from the perspective of time-frequency analysis. These solitons are associated with vector bundles of higher rank, expressed in terms of vector-valued Gabor frames. We apply the duality theory of Gabor analysis to show that Gaussians are such solitons for any value of a topological charge. Also they solve self/anti-self duality equations resulting from an energy functional for projections over noncommutative tori, and have a reformulation in terms of Gabor frames. As a consequence, the projections generated by Gaussians minimize the energy functional. We also comment on the case of the Moyal plane and the associated continuous vector-valued Gabor frames and show that Gaussians are the only class of solitons there.

中文翻译：

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非交换环面上的一般拓扑电荷孤子

我们从时频分析的角度研究了非交换环面上的一般拓扑电荷孤子。这些孤子与更高等级的向量束相关联，用向量值 Gabor 框架表示。我们应用 Gabor 分析的对偶理论来表明，对于任何拓扑电荷值，高斯都是这样的孤子。他们还解决了由非交换环上投影的能量泛函产生的自/反自对偶方程，并根据 Gabor 框架进行了重新表述。因此，高斯生成的投影使能量泛函最小化。我们还评论了 Moyal 平面和相关的连续向量值 Gabor 框架的情况，并表明高斯是那里唯一的孤子类别。