We investigate the inhomogeneous higher-order nonlinear Schrödinger (INHLS) equation including cubic–quintic–septic (CQS) nonlinear terms and gain or loss with variable coefficients. The exact analytic solution that describes dark soliton-type pulse propagation is found for the model by employing the ansatz method. Unlike the traditional \(\text {tanh}\) dark soliton in Kerr-type media, the functional form of this novel dark-managed soliton structure takes a \(\text {sech}^{2/3}\) profile. Parametric conditions are presented in which these optical solitons exist. We also investigated the stability of these dark-managed solitons under some initial perturbations by employing the numerical simulation methods. Finally, the interaction dynamics of two and three dark-managed solitons has been numerically explored.

我们研究了不均匀的高阶非线性Schrödinger（INHLS）方程，其中包括三次-五次-化粪池（CQS）非线性项以及具有可变系数的损益。通过使用ansatz方法，为模型找到了描述暗孤子型脉冲传播的精确解析解。与Kerr型介质中的传统\（\ text {tanh} \）暗孤子不同，这种新颖的暗管理孤子结构的功能形式采用\（\ text {sech} ^ {2/3} \）轮廓。提出了存在这些光学孤子的参数条件。我们还使用数值模拟方法研究了这些暗管理孤子在某些初始扰动下的稳定性。最后，对两个和三个暗管理孤子的相互作用动力学进行了数值研究。