In this paper, we performed analytical, numerical and experimental studies on the generation of soliton waves in discrete nonlinear transmission lines (NLTL) with varactors, as well as the analysis of the losses impact on the propagation of these waves. Using the reductive perturbation method, we derived a nonlinear Schrödinger (NLS) equation with a loss term and determined an analytical expression that completely describes the bright soliton profile. Our theoretical analysis predicts the carrier wave frequency threshold above which a formation of bright solitons can be observed. We also performed numerical simulations to confirm our analytical results and we analyzed the space–time evolution of the soliton waves. A good agreement between analytical and numerical findings was obtained. An experimental prototype of the lossy NLTL, built at the discrete level, was used to validate our proposed model. The experimental shape of the envelope solitons is well fitted by the theoretical waveforms, which take into account the amplitude damping due to the losses in commercially available varactors and inductors used in a prototype. Experimentally observed changes in soliton amplitude and half–maximum width during the propagation along lossy NLTL are in good accordance with the proposed model defined by NLS equation with loss term.

中文翻译：

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微波频率下有损非线性传输线中的孤子波：分析、数值和实验研究

在本文中，我们对具有变容二极管的离散非线性传输线 (NLTL) 中孤子波的产生进行了分析、数值和实验研究，并分析了对这些波传播的损耗影响。使用还原微扰方法，我们导出了一个带有损失项的非线性薛定谔 (NLS) 方程，并确定了一个完全描述明亮孤子轮廓的解析表达式。我们的理论分析预测了载波频率阈值，高于该阈值可以观察到明亮孤子的形成。我们还进行了数值模拟以确认我们的分析结果，并分析了孤子波的时空演化。获得了分析结果和数值结果之间的良好一致性。有损NLTL的实验原型，在离散级别构建，用于验证我们提出的模型。包络孤子的实验形状与理论波形非常吻合，其中考虑了由于原型中使用的市售变容二极管和电感器的损耗引起的振幅阻尼。实验观察到的孤子振幅和半最大宽度在沿有损 NLTL 传播过程中的变化与由 NLS 方程定义的具有损耗项的拟议模型非常吻合。