In this paper, we study the following linearly coupled system [Formula: see text], where ε > 0 is a small parameter, Pi (x) are positive potentials, and λij = λji > 0 (i ≠ j) are coupling constants for i, j = 1, …, N. We investigate the effect of potentials to the structure of the solutions. More precisely, we construct multi-spikes solutions concentrating near the local maximum point [Formula: see text] of Pi (x). When [Formula: see text], [Formula: see text], the components have spikes clustering at the same point as ε → 0+. When [Formula: see text], the components have spikes clustering at the different points as ε → 0+.

中文翻译：

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薛定谔方程线性耦合系统的分离和同步矢量解

在本文中，我们研究以下线性耦合系统[公式：见正文]，其中 ε > 0 是一个小参数，Pi (x) 是正电位，λij = λji > 0 (i ≠ j) 是耦合常数i, j = 1, ..., N。我们研究了势对解结构的影响。更准确地说，我们构建了集中在 Pi (x) 的局部最大值点 [公式：见正文] 附近的多尖峰解决方案。当[公式：见正文]、[公式：见正文]时，成分在ε→0+的同一点有尖峰聚集。当[公式：见正文]时，组件在不同点处具有尖峰聚类，为 ε → 0+。