We investigate the dynamics of optical soliton formation in media with quadratic nonlinearity under conditions of long-living oscillations produced by the soliton's internal modes. We compare the predictions of the second-order perturbation approach, combining it with the energy conservation law, with the direct numerical simulations using the transparent boundary conditions. We demonstrate that these two approaches correlate well and describe the nonlinear radiation damping of the internal modes.
(c) 2003 American Institute of Physics.