title: Segregated and synchronized vector solutions to linearly coupled systems of Schrödinger equations.
abstract: 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, andλij=λji> 0 (i≠j) are coupling constants fori,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] ofPi(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+.
authors.affiliation: College of Mathematics and Information Science, Jiangxi Normal University , Nanchang, Jiangxi 330022, People's Republic of China.
authors.forename: Wei
authors.initials: W
authors.lastname: Long
authors.affiliation: School of Mathematics and Statistics, Central China Normal University , Wuhan 430079, People's Republic of China.
authors.forename: Qingfang
authors.initials: Q
authors.lastname: Wang