Scattering of matter-waves in spatially inhomogeneous environments

We study scattering of quasi one-dimensional matter-waves at an interface of two spatial domains, one with repulsive and one with attractive interatomic interactions. It is shown that the incidence of a Gaussian wavepacket from the repulsive to the attractive region gives rise to generation of a soliton train. More specifically, the number of emergent solitons can be controlled e.g. by the variation of the amplitude or the width of the incoming wavepacket. Furthermore, we study the reflectivity of a soliton incident from the attractive region to the repulsive one. We find the reflection coefficient numerically and employ analytical methods, that treat the soliton as a particle (for moderate and large amplitudes) or a quasi-linear wavepacket (for small amplitudes), to determine the critical soliton momentum - as function of the soliton amplitude - for which total reflection is observed.