  We study the following coupled Schr\"{o}dinger equations which have appeared
as several models from mathematical physics: \begin{displaymath}
\begin{cases}-\Delta u_1 +\la_1 u_1 = \mu_1 u_1^3+\beta u_1 u_2^2, \quad x\in
\Omega,\\ -\Delta u_2 +\la_2 u_2 =\mu_2 u_2^3+\beta u_1^2 u_2, \quad x\in
\Om,\\ u_1=u_2=0 \,\,\,\hbox{on \,$\partial\Om$}.\end{cases}\end{displaymath}
Here $\Om\subset\RN (N=2, 3)$ is a smooth bounded domain, $\la_1, \la_2$,
$\mu_1, \mu_2$ are all positive constants. We show that, for each
$k\in\mathbb{N}$ there exists $\bb_k>0$ such that this system has at least $k$
sign-changing solutions (i.e., both two components change sign) and $k$
semi-nodal solutions (i.e., one component changes sign and the other one is
positive) for each fixed $\bb\in (0, \bb_k)$.
