Dark-bright soliton interactions in coupled nonautonomous nonlinear Schrödinger equation with complex potentials

•Soliton dynamics in presence of complex potentials is presented using coupled nonlinear Schrödinger equation.•The external potential brings about notable changes in the dynamics of soliton by changing it’s velocity, frequency and the wave number.•Nonlinear soliton tunneling and non trivial soliton amplifications are demonstrated using three-soliton solution of the proposed model.•It is possible to tune soliton intensity vis–vis barrier height via inelastic soliton interaction. We investigate dark-bright soliton dynamics in a coupled nonlinear Schrödinger equation in presence of complex potentials and the associated spectral problem. Using asymptotic analysis and graphical analysis, we study the interactions of soliton complexes under different potentials. We present the results of elastic and inelastic interaction between solitons in presence of the potentials. The external potential brings about notable changes in the dynamics of soliton by changing it’s velocity, frequency and the wave number. The changes are however, same on the all the solitons and hence the external potential do not alters the conditions of the elastic interaction. We also present interesting features of complex three soliton interactions under the complex potentials. The shape change may occur even when there is no relative velocity between solitons. We hope that the present analysis would be useful for a better understanding of soliton interactions in an inhomogeneous nonlinear fiber and the dynamics of condensates in atomic physics.