Vector solitons and localized waves of two coupled nonlinear Schrödinger equations in the nonlinear electrical transmission line lattice

IF 2.1 3区物理与天体物理 Q2 ACOUSTICS

Wave Motion Pub Date : 2025-03-14 DOI:10.1016/j.wavemoti.2025.103540

Alphonse Houwe , Souleymanou Abbagari , Lanre Akinyemi , Serge Yamigno Doka

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Abstract

The study examines modulation instability and localized wave structures in a nonlinear electrical transmission line with next-neighbor couplings. By employing an expansion method, coupled nonlinear Schrödinger equations are derived to analyze the system. The influence of next-neighbor coupling on the perturbed plane wave is highlighted, demonstrating unstable modes arising from modulation instability. Notably, a stronger next-neighbor coupling significantly enhances the amplitude of modulation instability, confirming that the nonlinear electrical lattice supports localized nonlinear waves. Analytical analysis, considering the self-phase modulation parameter, reveals the existence of three types of coupled soliton modes: bright-bright solitons, dark-bright solitons, and bright-dark solitons, influenced by the nearest neighbor coupling. Numerical simulations further illustrate the development of modulation instability through modulated wave patterns. Additionally, at a specific propagation time, another structure is identified, confirming the formation of rogue waves with crests and troughs in the network. These wave phenomena are characteristic of nonlinear systems where dispersion and nonlinearity interact.

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非线性传输线晶格中两个耦合非线性Schrödinger方程的矢量孤子和局域波

研究了具有邻域耦合的非线性输电线路中的调制不稳定性和局域波结构。采用展开法推导了耦合非线性Schrödinger方程，对系统进行了分析。强调了相邻耦合对扰动平面波的影响，证明了调制不稳定引起的不稳定模式。值得注意的是，更强的相邻耦合显著增强了调制不稳定性的幅度，证实了非线性电晶格支持局域非线性波。考虑自相位调制参数的解析分析表明，受最近邻耦合的影响，存在亮-亮孤子、暗-亮孤子和亮-暗孤子三种耦合模式。数值模拟进一步说明了通过调制波形调制不稳定性的发展。此外，在特定的传播时间，另一种结构被识别出来，证实了网络中具有波峰和波谷的异常波的形成。这些波动现象是色散和非线性相互作用的非线性系统的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Wave Motion 物理-力学

CiteScore

4.10

自引率

8.30%

发文量

118

审稿时长

3 months

期刊介绍： Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.