  We study the following nonlinear Schr\"{o}dinger equation $$ iu_t=-\Delta
u+V(x)u-a|u|^qu \quad (t,x)\in \mathbb{R}^1\times \mathbb{R}^2, $$ where $a>0,
\ q\in(0,2)$ and $V(x)$ is some type of trapping potentials. For any fixed
$a>a^*:= \|Q\|_2^2$, where $Q$ is the unique (up to translations) positive
radial solution of $\Delta u-u+u^3=0$ in $\mathbb{R}^2$, by directly using
constrained variational method and energy estimates we present a detailed
analysis of the concentration and symmetry breaking of the standing waves for
the above equation as $q\nearrow 2$.
