  We discuss the possible observation of a new type of standing nonlinear
atomic matter wave in the condensate: the nonlinear impurity mode. It is
investigated dynamical effects of a bright soliton in Bose-Einstein-condensed
(BEC) systems with local space variations of the two-body atomic scattering
length. A rich dynamics is observed in the interaction between the soliton and
an inhomogeneity. Processes as trapping, reflection and transmission of the
bright matter soliton due to the impurity are studied considering an analytical
time-dependent variational approach and also by full numerical simulation. A
condition is obtained for the collapse of the bright solitary wave in the
quasi-one-dimensional BEC with attractive local inhomogeneity.
