In this paper, we consider the following weakly coupled nonlinear Schr\"{o}dinger system in $\mathbb{R}^N$ $$ \left\{ \begin{array}{ll} -\varepsilon^{2}\Delta u_1 + V_1(x)u = |u|^{2p - 2}u_1 + b|u|^{p - 2}|v|^pu, & x\in \mathbb{R}^N,\vspace{0.12cm} -\varepsilon^{2}\Delta u_2 + V_2(x)v = |v|^{2p - 2}u_2 + b|v|^{p - 2}|u|^pv, & x\in \mathbb{R}^N, \end{array} \right. $$ where $\varepsilon>0$, $b\in\mathbb{R}$ is a coupling constant, $2p\in (2 + \frac{2\sigma}{N - 2}, 2^*)$ with $\sigma \in[0,1]$, $2^* = 2N/(N - 2),\ N\geq 3$, $V_1$ and $V_2$ belong to $C(\mathbb{R}^N,[0,\infty))$. This type of systems arise in models of nonlinear optics. Let $\min_{i = 1,2}\liminf_{|x|\to\infty}V_i(x)|x|^{2\sigma} > 0$. We prove the problem has a family of nontrivial solutions $\{w_{\varepsilon} = (u_{\varepsilon},v_{\varepsilon}):0<\varepsilon<\varepsilon_{0}\}$ that concentrate at the prescribed common local minimum of $\Lambda_1 = \Lambda_2$ provided that $b>b_{\omega} > 0$ an 查看全文>>