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 syste...

中文翻译：

---

具有分布系数的立方五次耗散Gross-Pitaevskii方程的调制不稳定性和孤子控制

在这项工作中，我们考虑了广义立方-五次耗散的Gross-Pitaevskii方程，该方程控制了具有二体和三体原子间相互作用的Bose-Einstein凝聚体中物质波孤子的动力学，其时空相关的耗散势由抛物线形，线性和复杂项。通过使用ansatz方法，在某些参数条件下给出了调制不稳定性以及灰度，扭结和亮孤子解。我们发现，与凝结物的进料或原子损失有关的复杂电势严重地改变了不稳定性和稳定性域，而线性电势对系统的稳定性没有影响。通过使用精确的类孤子分析解决方案，我们对孤子控制系统进行了分析研究，结果表明，孤子控制系统可以放宽对参数条件的限制。我们发现物质波孤子在系统中的运动...