  We investigate the structure of nodal solutions for coupled nonlinear
Schr\"{o}dinger equations in the repulsive coupling regime. Among other
results, for the following coupled system of $N$ equations, we prove the
existence of infinitely many nodal solutions which share the same
componentwise-prescribed nodal numbers \begin{equation}\label{ab}
  \left\{
  \begin{array}{lr}
  -{\Delta}u_{j}+\lambda u_{j}=\mu u^{3}_{j}+\sum_{i\neq j}\beta u_{j}u_{i}^{2}
\,\,\,\,\,\,\, in\ \W ,
  u_{j}\in H_{0,r}^{1}(\W), \,\,\,\,\,\,\,\,j=1,\dots,N,
  \end{array}
  \right. \end{equation} where $\W$ is a radial domain in $\mathbb R^n$ for
$n\leq 3$, $\lambda>0$, $\mu>0$, and $\beta <0$. More precisely, let $p$ be a
prime factor of $N$ and write $N=pB$. Suppose $\beta\leq-\frac{\mu}{p-1}$. Then
for any given non-negative integers $P_{1},P_{2},\dots,P_{B}$, (\ref{ab}) has
infinitely many solutions $(u_{1},\dots,u_{N})$ such that each of these
solutions satisfies the same property: for $b=1,...,B$, $u_{pb-p+i}$ changes
sign precisely $P_b$ times for $i=1,...,p$. The result reveals the complex
nature of the solution structure in the repulsive coupling regime due to
componentwise segregation of solutions. Our method is to combine a heat flow
approach as deformation with a minimax construction of the symmetric mountain
pass theorem using a $\mathbb Z_p$ group action index. Our method is robust,
also allowing to give the existence of one solution without assuming any
symmetry of the coupling.
