Segregated and synchronized vector solutions to linearly coupled systems of Schrodinger equations

In this paper, we study the following linearly coupled system -epsilon(2)Delta u(i) + P-i(x)u(i) = u(i)(3) + Sigma(N)(j not equal 1) lambda(i,j)u(j), u(i) epsilon H-1 (R-3), i = 1,..., N, where epsilon > 0 is a small parameter, P-i(x) are positive potentials, and lambda(ij) =lambda(ij) > 0 (i not equal 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 x(0)(i) of P-i(x). When x(0)(i) = x(0)(j), P-i(x(0)(i)) = P-j( x(0)(j)) = a, i not equal j, i, j = 1,..., N, the components have spikes clustering at the same point as epsilon -> 0(+). When x(0)(i) not equal x(0)(j), i not equal j, the components have spikes clustering at the different points as epsilon -> 0(+). (C) 2015 AIP Publishing LLC.