非线性传输线中电容参数对孤子行为的影响
Effect of Capacitance Parameters on Soliton Behaviors in Nonlinear Transmission Lines
DOI: 10.12677/AAM.2023.122065, PDF,    国家自然科学基金支持
作者: 梁雨珂, 吴颉尔, 周 昱*：江苏科技大学理学院，江苏 镇江；罗文琛：中南大学物理与电子学院，湖南 长沙
关键词: 同伦分析法；非线性传输线路；孤子解；谐振参数；Homotopy Analysis Method； Nonlinear Transmission Lines； Soliton Solutions； Resonant Parameters
摘要: 基于同伦分析法研究了非线性传输线系统中电容参数和谐振参数对体系孤子行为的影响，在弱非线性情况下将所得解与数值解进行对比，验证了系统的孤子行为。在强非线性情况下，通过考虑非线性电容表达式中各项参数的不同变化，找出孤子半峰全宽与这些参数的关系，表明可通过改变非线性电容表达式各项参数以及谐振参数，调控在非线性传输线中的孤子行为，也可以通过对谐振参数和非线性参数的调节，改变孤子解半峰全宽，实现对非线性传输线的非线性行为研究。
Abstract: The influence of capacitance parameters and resonance parameters on the soliton behavior of non-linear transmission line system is studied based on homotopy analysis method. In the weakly non-linearity case, the obtained solution is compared with the numerical solution to verify the soliton behavior of the system while in the strongly nonlinearity case, the relationship between the full width at half maximum of soliton solution and these parameters is found by considering the differ-ent changes of various parameters in the nonlinear capacitance expression. It shows that the be-havior of soliton in the nonlinear transmission line can be controlled by changing the parameters of the nonlinear capacitance expression and the resonance parameters, and the full width at half maximum of soliton solution can also be changed by adjusting the resonance parameters and non-linear parameters. The nonlinear behaviors of the nonlinear transmission lines could be partially understood based on our work.
文章引用：梁雨珂, 吴颉尔, 周昱, 罗文琛. 非线性传输线中电容参数对孤子行为的影响[J]. 应用数学进展, 2023, 12(2): 615-625. https://doi.org/10.12677/AAM.2023.122065

参考文献

[1] Liu, J.G., Osman, M.S., Zhu, W.H., et al. (2019) Different Complex Wave Structures Described by the Hirota Equation with Variable Coefficients in Inhomogeneous Optical Fibers. Applied Physics B, 125, 175. [Google Scholar] [CrossRef] 
[2] Osman, M.S. (2019) New Analytical Study of Water Waves De-scribed by Coupled Fractional Variant Boussinesq Equation in Fluid Dynamics. Pramana–Journal of Physics, 93, 26. [Google Scholar] [CrossRef] 
[3] Hirota, R., Hu, X.B. and Tang, X.Y. (2003) A Vector Potential KdV Equation and Vector Ito Equation: Soliton Solutions, Bilinear Bäcklund Transformations and Lax Pairs. Journal of Mathematical Analysis and Applications, 288, 326-348. [Google Scholar] [CrossRef] 
[4] Wadati, M. (1975) Wave Propagation in Nonlinear Lattice. I. Journal of the Physical Society of Japan, 38, 673-680. [Google Scholar] [CrossRef] 
[5] Sullivan, J.M., Twardowski, M.S., Ronald, J., et al. (2013) Measuring Optical Backscattering in Water. In: Light Scattering Reviews, Vol. 7, Springer, Berlin, 189-224. [Google Scholar] [CrossRef] 
[6] Zeng, Y. and Dai, H. (2001) Constructing N-Soliton Solution for the mKdV Equation through Constrained Flows. Journal of Physics A: Mathematical and General, 34, L657. [Google Scholar] [CrossRef] 
[7] Inc, M. (2007) An Approximate Solitary Wave Solution with Compact Support for the Modified KdV Equation. Applied Mathematics and Computation, 184, 631-637. [Google Scholar] [CrossRef] 
[8] Wazwaz, A.M. (2007) The Extended Tanh Method for Abundant Solitary Wave Solutions of Nonlinear Wave Equations. Applied Mathematics and Computation, 187, 1131-1142. [Google Scholar] [CrossRef] 
[9] Guo, Y.F., Dai, Z.D. and Li, D. (2009) New Exact Periodic Soli-tary-Wave Solution of MKdV Equation. Communications in Nonlinear Science and Numerical Simulation, 14, 3821-3824. [Google Scholar] [CrossRef] 
[10] Parkes, E.J. (2010) Observations on the Tanh-Coth Expansion Method for Finding Solutions to Nonlinear Evolution Equations. Applied Mathematics and Computation, 217, 1749-1754. [Google Scholar] [CrossRef] 
[11] Zhang, J., Zhang, D. and Shen, Q. (2011) Bilinear Ap-proach for a Symmetry Constraint of the Modified KdV Equation. Applied Mathematics and Computation, 218, 4494-4500. [Google Scholar] [CrossRef] 
[12] Yin, J.L., Xing, Q.Q. and Tian, L.X. (2014) Complex Dynamical Behaviors of Compact Solitary Waves in the Perturbed mKdV Equation. Chinese Physics B, 23, Article ID: 080201. [Google Scholar] [CrossRef] 
[13] Fukushima, K., Wadati, M. and Narahara, Y. (1980) Envelope Solition in a New Nonlinear Transmission Line. Journal of the Physical Society of Japan, 49, 1593-1597. [Google Scholar] [CrossRef] 
[14] Benton, E.R. and Platzman, G.W. (1972) A Table of Solutions of the One-Dimensional Burgers Equation. Quarterly of Applied Mathematics, 30, 195-212. [Google Scholar] [CrossRef] 
[15] Kumar, H. and El-Ganaini, S. (2020) Traveling and Localized Solitary Wave Solutions of the Nonlinear Electrical Transmission Line Model Equation. The European Physical Journal Plus, 135, 1-25. [Google Scholar] [CrossRef] 
[16] Duan, W.-S., et al. (2002) Weakly Two-Dimensional Soli-tary Waves on Coupled Nonlinear Transmission Lines. Chinese Physics Letters, 19, 1231. [Google Scholar] [CrossRef] 
[17] French, D.M. and Hoff, B.W. (2014) Spatially Dispersive Ferrite Nonlinear Transmission Line with Axial Bias. IEEE Transactions on Plasma Science, 42, 3387-3390. [Google Scholar] [CrossRef] 
[18] Kuek, N.S., Liew, A.C., Schamiloglu, E., et al. (2013) Pulsed RF Oscillations on a Nonlinear Capacitive Transmission Line. IEEE Transactions on Dielectrics and Electrical Insulation, 20, 1129-1135. [Google Scholar] [CrossRef] 
[19] French, D.M., Lau, Y.Y. and Gilgenbach, R.M. (2010) High Power Nonlinear Transmission Lines with Nonlinear Inductance. 2010 IEEE International Power Modulator and High Voltage Conference, Atlanta, 23-27 May 2010, 598-599. [Google Scholar] [CrossRef] 
[20] Kuek, N.S., Liew, A.C., Schamiloglu, E., et al. (2014) RF Pulse Generator Based on a Nonlinear Hybrid Line. IEEE Transactions on Plasma Science, 42, 3268-3273. [Google Scholar] [CrossRef] 
[21] Liao, S. (2004) On the Homotopy Analysis Method for Nonlinear Problems. Applied Mathematics and Computation, 147, 499-513. [Google Scholar] [CrossRef] 
[22] 廖世俊, 刘曾. 同伦分析方法进展综述[J]. 力学进展, 2019, 49(1): 237-273.
[23] Afshari, E. and Hajimiri, A. (2005) Nonlinear Transmission Lines for Pulse Shaping in Sil-icon. IEEE Journal of Solid-State Circuits, 40, 744-752. [Google Scholar] [CrossRef] 

为你推荐