On multichannel solutions of nonlinear Schr\"{o}dinger equations: algorithm, analysis and numerical explorations

We apply the method of modulation equations to numerically solve the NLS with multichannel dynamics, given by a trapped localized state and radiation. This approach employs the modulation theory of Soffer-Weinstein, which gives a system of ODE's coupled to the radiation term, which is valid for all times. We comment on the differences of this method from the well-known method of collective coordinates.