  We consider the following system of Schr\"odinger equations
\begin{equation*}\left.\begin{cases}
  -\Delta U + \lambda U = \alpha_0 U^3+ \beta UV^2
  -\Delta V + \mu(y) V = \alpha_1 V^3+\beta U^2V \end{cases}\right. \text{in}
\quad \mathbb{R}^N, \ N=2, 3,\end{equation*} where $\lambda$, $\alpha_0$,
$\alpha_1>0$ are positive constants, $\beta \in \mathbb{R}$ is the coupling
constant, and $\mu: \mathbb{R}^N \rightarrow \mathbb{R}$ is a potential
function. Continuing the work of Lin and Peng \cite{lin_peng_2014}, we present
a solution of the type where one species has a peak at the origin and the other
species has many peaks over a circle, but as seen in the above, coupling terms
are nonlinear.
