In the present paper we survey some recents results concerning existence of semiclassical standing waves solutions for nonlinear Schrödinger equations. Furthermore, from Maxwell's equations we derive a nonlinear Schrödinger equation which represents a model of propagation of an electromagnetic field in optical waveguides.

We obtain some microlocal estimates of the resonant states associated to a resonance $z_0$ of an $h$-differential operator. More precisely, we show that the normalized resonant states are $𝒪(\sqrt{|\mathrm{Im}{z}_0|/h}$$+h^{\infty }...$