“…Numerous theoretical studies [ 13 , 14 , 15 , 16 , 17 , 18 , 19 ] have already been carried out to study the interaction mechanism between the impurity and the excitations. These studies, however, mainly involve linear excitations and an impurity with an infinite mass [ 13 , 14 , 15 , 16 , 17 , 18 , 19 ] or finite effective mass [ 20 ]. Thus, it is highly desired to study the interaction mechanism between a quantum impurity with a finite effective mass and nonlinear excitations, such as the soliton, which is not only a key ingredient in the effective field theory, but also plays an important role in information processing [ 21 ].…”