Wen Xiao-Yong, Yan Zhenya, Zhang Guoqiang
Department of Mathematics, School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, People's Republic of China.
KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
Proc Math Phys Eng Sci. 2020 Oct;476(2242):20200512. doi: 10.1098/rspa.2020.0512. Epub 2020 Oct 28.
The nonlinear self-dual network equations that describe the propagations of electrical signals in nonlinear LC self-dual circuits are explored. We firstly analyse the modulation instability of the constant amplitude waves. Secondly, a novel generalized perturbation (, - )-fold Darboux transform (DT) is proposed for the lattice system by means of the Taylor expansion and a parameter limit procedure. Thirdly, the obtained perturbation (1, - 1)-fold DT is used to find its new higher-order rational solitons (RSs) in terms of determinants. These higher-order RSs differ from those known results in terms of hyperbolic functions. The abundant wave structures of the first-, second-, third- and fourth-order RSs are exhibited in detail. Their dynamical behaviours and stabilities are numerically simulated. These results may be useful for understanding the wave propagations of electrical signals.
研究了描述非线性LC自对偶电路中电信号传播的非线性自对偶网络方程。我们首先分析了等幅波的调制不稳定性。其次，通过泰勒展开和参数极限过程，为晶格系统提出了一种新颖的广义微扰(, - )-重达布变换(DT)。第三，利用得到的微扰(1, - 1)-重DT，通过行列式求出其新的高阶有理孤子(RS)。这些高阶RS在双曲函数方面与已知结果不同。详细展示了一阶、二阶、三阶和四阶RS丰富的波结构。对它们的动力学行为和稳定性进行了数值模拟。这些结果可能有助于理解电信号的波传播。
