The present work describes the behavior of solitary and periodic waves in a nonlinear electrical transmission line with linear dispersion. Based on the semidiscrete approximation, we show that the dynamics of modulated wave in the system can be described by an extended cubic-quintic nonlinear Schrödinger equation. Using a simple transformation, we reduce the given equation to a cubic-quintic Duffing oscillator equation. By means of the method of dynamical systems, we obtain bifurcations of the phase portraits of the traveling wave under different parameter conditions. Corresponding to the various phase portrait trajectories, we derive possible exact explicit parametric representations of solutions. The results of our study demonstrate that the additional imprint phase in the signal voltage leads to a number of interesting solitary-wave solutions, e.g., gray soliton and anti-gray soliton, which have not been observed for the same model without this parameter. These new obtained solutions are useful in better understanding of the dynamic of the considered network as well as of other systems that can be governed by a cubic-quintic nonlinear Schrödinger equation model.

目前的工作描述了具有线性色散的非线性电力传输线中孤立波和周期波的行为。基于半离散近似，我们表明系统中调制波的动力学可以用扩展的三次五次非线性薛定谔方程来描述。使用简单的变换，我们将给定的方程简化为三次五次 Duffing 振荡器方程。借助动力学系统的方法，我们得到了不同参数条件下行波相图的分岔。对应于各种相图轨迹，我们推导出解决方案的可能的精确显式参数表示。我们的研究结果表明，信号电压中的额外印记相位导致了许多有趣的孤立波解决方案，例如，灰色孤子和反灰色孤子，在没有这个参数的情况下，对于同一模型没有观察到。这些新获得的解有助于更好地理解所考虑的网络以及可由三次五次非线性薛定谔方程模型控制的其他系统的动态。