Abstract
Soliton, by definition, is a non-linear collective dynamics, exhibiting a non-dispersive wavefront during its propagation in space. A direct but nontrivial question is how stable a soliton can be against collisions with a disorder potential and to what extent the nonlinearity changes the qualitative behaviour of the scattering. In this work, we systematically investigate the scattering of bright solitons through a simple delta function defect. Different from existing literature, we present a global phase diagram of transmission coefficients and derive the phase boundary for transition of quantum reflection/transmission. Moreover, we give a necessary condition for the existence of bound states using simple arguments. Finally, we proposed a practical model that captures the location of this transition in the phase diagram.