Asymptotic description of nonlinear resonance

We study a hard regime of stimulation of two-frequency oscillations in the main resonance equation with a fast oscillating external force: $ \ve i \psi' + |\psi|^2\psi = \exp\big(it^2/ (2\ve)\big), 0<\ve\ll1$. This phenomenon is caused by resonance between an eigenmode and the external force. The asymptotic solution before, inside and after the resonance layer is studied in detail and matched.