Scattering of Linear Waves on a Soliton

We have shown that the wave scattering by a soliton of nonlinear Schrödinger equation occurs in a peculiar way. The nonlinear interaction leads to the generation of waves with frequencies that are multiples of the frequency of the incident wave, minus the frequency of the soliton, while the soliton experiences growth due to the absorption of particles from the incoming wave. We propose an analytical approach based on the Born approximation to calculate the amplitudes of scattered waves and, consequently, the number of particles absorbed by the soliton. This approach is validated through direct comparison with the results of numerical simulation.