  We consider asymptotic stability of a small solitary wave to supercritical
2-dimensional nonlinear Schr\"{o}dinger equations $$ iu_t+\Delta u=Vu\pm
|u|^{p-1}u \quad\text{for $(x,t)\in\mathbb{R}^2\times\mathbb{R}$,}$$ in the
energy class.
