Interaction of soliton with sinusoidal wave packet

The interaction of a soliton of the Nonlinear Schrodinger Equation (NSE) with a weak sinusoidal wave packet is treated analytically. The second-order soliton solution containing the original soliton and a perturbing soliton is expanded to first order in the amplitude of the perturbating soliton. From this expansion, one obtains the associate function of Gordon (1992) and a continuous change of position and phase of the perturbed soliton. One finds that the soliton experiences a second-order change of velocity under the influence of the perturbation. This result is then used to derive the displacement due to a wave packet of general shape, which is also confirmed by computer simulation.