PARTICLE AND WAVE PROPERTIES OF SOLITONS - RESONANT AND NONRESONANT SOLITON SCATTERING BY IMPURITIES

Dynamics of many systems of interacting quasiparticles can be described in the mean field approximation by the nonlinear Schrödinger equation (NSE). The bound state of a larger number of quasiparticles in such a system is equivalent to a dynamical soliton, its amplitude being proportional to the number of bound quasiparticles. Soliton dynamics in the presence of impurities is analyzed. In adiabatic approximation soliton dynamics is similar to classical dynamics of a particle, moving in the effective potential field. But the adiabatic approximation becomes inadequate when the scattering of a rather fast soliton by point impurities is studied, and the scattering intensity is characterized by the reflection coefficient. The reflection coefficient of the soliton is calculated in the Born approximation of the perturbation theory based on the inverse scattering technique. An analytical comparison with the scattering of linear wave packet is carried out. In particular, we analytically describe the nonlinear resonant scattering by two point impurities. © 1990.