  We study the dispersion mechanism of Lieb mode excitations of both single and
multi component ultra-cold atomic Bose gas, subject to a harmonic confinement
through chirp management. It is shown that in some parameter domain, the
hole-like excitations lead to the soliton's negative mass regime, arising due
to the coupling between chirp momentum and Kohn mode. In low momenta region the
trap considerably affects the dispersion of the grey soliton, which opens a new
window to observe Lieb-mode excitations. Further, we extend our analysis to
binary condensate, which yields usual shape compatible grey-bright soliton
pairs. The inter-species interaction induces a shift in the Lieb-mode
excitations, where the pair can form a bound state. We emphasize that the
present model provides an opportunity to study such excitations in the low
momenta regime, as well as the formation of bound state in binary condensate.
