Modulational instability and soliton control in a cubic–quintic dissipative Gross–Pitaevskii equation with distributed coefficients*

Abstract

Abstract In this work, we consider the generalized cubic–quintic dissipative Gross–Pitaevskii equation, which governs the dynamics of matter wave solitons in Bose–Einstein condensates with two- and three-body interatomic interactions in a spatiotemporal-dependent dissipative potential consisting of parabolic, linear, and complex terms. By using the ansatz method, the modulational instability and gray, kink, and bright soliton solutions are presented under certain parametric conditions. We found that the complex potential, related to the feeding or the loss of atoms by the condensates seriously modifies the instability and stability domain, while the linear potential has not effect on the stability of the system. With the use of exact analytical soliton-like solutions, we investigate analytically the solitons control system, and the results show that the soliton control system may relax the limitations to parametric conditions. We found that the motion of matter wave solitons in the systems can be manipulated by controlling both the external harmonic and linear trapping potentials. We have established that the amplitude of the matter wave solitons keep no change in propagating in the system though the total number of the condensate atoms decreases (increases) when the condensate losses (gains) atoms. We also showed that the three-body interatomic interactions is responsible of the soliton compression. Our results also revealed that the found exact soliton-like solutions can be used to describe the compression of matter wave solitons in BEC system with loss of atoms.