Research article Special Issues

New complex wave patterns to the electrical transmission line model arising in network system

  • Received: 04 October 2019 Accepted: 18 January 2020 Published: 18 February 2020
  • MSC : 35Axx, 34Axx

  • This study reveals new voltage behaviors to the electrical transmission line equation in a network system by using the newly presented sine-Gordon equation function method. It is commented about these behaviors which come from different simulations of results obtained in this paper. Many illustrations are offered to validate our analytical results. Linear stability analysis is also investigated in a detailed manner.

    Citation: Wei Gao, Mine Senel, Gulnur Yel, Haci Mehmet Baskonus, Bilgin Senel. New complex wave patterns to the electrical transmission line model arising in network system[J]. AIMS Mathematics, 2020, 5(3): 1881-1892. doi: 10.3934/math.2020125

    Related Papers:

  • This study reveals new voltage behaviors to the electrical transmission line equation in a network system by using the newly presented sine-Gordon equation function method. It is commented about these behaviors which come from different simulations of results obtained in this paper. Many illustrations are offered to validate our analytical results. Linear stability analysis is also investigated in a detailed manner.


    加载中


    [1] H. Y. Donkeng, F. Kenmogne, D. Yemele,et al., Modulated compact-like pulse signals in a nonlinear electrical transmission line: A specific case studied, Chin. J. Phys., 55 (2017), 683-691. doi: 10.1016/j.cjph.2017.04.011
    [2] K. A. Abro, I. Khan, K. S. Nisar, Novel technique of Atangana and Baleanu for heat dissipation in transmission line of electrical circuit, Chaos Sol. Fract., 129 (2019), 40-45. doi: 10.1016/j.chaos.2019.08.001
    [3] H. L. Zhen, B. Tian, H. Zhong, et al., Dynamic behaviors and soliton solutions of the modified Zakharov-Kuznetsov equation in the electrical transmission line, Comput. Math. with Appl., 68 (2014), 579-588. doi: 10.1016/j.camwa.2014.06.021
    [4] A. B. T. Motcheyo, J. D. T. Tchameu, S. I. Fewo, et al., Chameleon's behavior of modulable nonlinear electrical transmission line, Commun Nonlinear Sci, 53 (2017), 22-30. doi: 10.1016/j.cnsns.2017.04.031
    [5] F. Kenmogne, D. Yemele, Exotic modulated signals in a nonlinear electrical transmission line: Modulated peak solitary wave and gray compacton, Chaos Sol. Fract., 45 (2012), 21-34. doi: 10.1016/j.chaos.2011.09.009
    [6] H. Kanaya, Y. Nakamura, R. K. Pokharela, et al., Development of electrically small planar antennas with transmission line based impedance matching circuit for a 2.4 GHz band, AEU-Int. J. Eletron. C., 65 (2011), 148-153. doi: 10.1016/j.aeue.2010.03.001
    [7] T. Kuusela, Soliton experiments in a damped ac-driven nonlinear electrical transmission line, Phys. Lett. A, 167 (1992), 54-59. doi: 10.1016/0375-9601(92)90625-V
    [8] R. Uklejewski, Analysis of transmission of vibrations in a porous vibroisolator on the basis of electrical transmission line theory, J. Sound Vib., 113 (1987), 9-16. doi: 10.1016/S0022-460X(87)81336-6
    [9] M. Senel, B. Senel, L. Bilir, et al., The relation between electricity demand and the economic and demographic state: A multiple regression analysis, J. Energy Dev., 38 (2013), 257-274.
    [10] E. Tala-Tebue, D. C. Tsobgni-Fozap, A. Kenfack-Jiotsa, et al., Envelope periodic solutions for a discrete network with the Jacobi elliptic functions and the alternative (G'/G)-expansion method including the generalized Riccati equation, Eur. Phys. J. Plus, 129 (2014), 1-10. doi: 10.1140/epjp/i2014-14001-y
    [11] E. Tala-Tebue, E. M. E. Zayed, New Jacobi elliptic function solutions, solitons and other solutions for the (2+1)-dimensional nonlinear electrical transmission line equation, Eur. Phys. J. Plus, 133 (2018), 1-7. doi: 10.1140/epjp/i2018-11804-8
    [12] C. Cattani, Harmonic wavelet solutions of the Schrodinger equation, Int. J. Fluid Mech., 30 (2003), 463-472. doi: 10.1615/InterJFluidMechRes.v30.i5.10
    [13] Z. Zhao, B. Han, Residual symmetry, Bucklund transformation and CRE solvability of a (2+1)- dimensional nonlinear system, Nonlinear Dyn., 94 (2018), 461-474. doi: 10.1007/s11071-018-4371-2
    [14] E. I. Eskitascioglu, M. B. Aktas, H. M. Baskonus, New complex and hyperbolic forms for AblowitzKaup-Newell-Segur wave equation with fourth order, Appl. Math. Nonlinear Sci., 4 (2019), 105-112.
    [15] A. Yokus, H. M. Baskonus, T. A. Sulaiman, et al., Numerical simulation and solutions of the two a component second order KdV evolutionary system, Numer. Math. Part. Dif. E., 34 (2018), 211-227. doi: 10.1002/num.22192
    [16] A. Yokus, T. A. Sulaiman, M. T. Gulluoglu, et al., Stability analysis, numerical and exact solutions of the (1+1)-dimensional NDMBBM equation, Numer. Math. Part. Dif. E., 22 (2018), 1-10.
    [17] Z. Zhao, B. Han, Lump solutions of a (3+1)-dimensional B-type KP equation and its dimensionally reduced equations, Anal. Math. Phys., 9 (2019), 119-130. doi: 10.1007/s13324-017-0185-5
    [18] C. Cattani, On the existence of wavelet symmetries in archaea DNA, Comput. Math. Method M., 2012 (2012), 1-21.
    [19] M. Guedda, Z. Hammouch, Similarity flow solutions of a non-newtonian power-law fluid, Int. J. Nonlinear Sci., 6 (2008), 255-264.
    [20] A. Prakash, M. Kumar, K. K. Sharma, Numerical method for solving coupled Burgers equation, Appl. Math. Comput., 260 (2015), 314-320.
    [21] M. Guedda, Z. Hammouch, On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers, Fluid Dyn. Res., 38 (2006), 211-223. doi: 10.1016/j.fluiddyn.2005.11.001
    [22] H. Rezazadeh, New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity, Optik, 167 (2018), 218-227. doi: 10.1016/j.ijleo.2018.04.026
    [23] C. Cattani, Haar wavelet-based technique for sharp jumps classification, Math. Comput. Model., 39 (2004), 255-278. doi: 10.1016/S0895-7177(04)90010-6
    [24] G. Yel, H. M. Baskonus, H. Bulut, Novel archetypes of new coupled Konno-Oono equation by using sine-Gordon expansion method, Opt. Quant. Electron., 49 (2017), 1-10. doi: 10.1007/s11082-016-0848-8
    [25] O. A. Ilhan, A. Esen, H. Bulut, et al., Singular solitons in the Pseudo-parabolic model arising in nonlinear surface waves, Results Phys., 12 (2019), 1712-1715. doi: 10.1016/j.rinp.2019.01.059
    [26] L. D. Moleleki, T. Motsepa, C. M. Khalique, Solutions and conservation laws of a generalized second extended (3+1)-dimensional Jimbo-Miwa equation, Applied Math. Nonlinear Sci., 3 (2018), 459-474. doi: 10.2478/AMNS.2018.2.00036
    [27] H. M. Baskonus, New acoustic wave behaviors to the Davey-Stewartson equation with power-law nonlinearity arising in fluid dynamics, Nonlinear Dyn., 86 (2016), 177-183. doi: 10.1007/s11071-016-2880-4
    [28] C. M. Khalique, I. E. Mhlanga, Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation, Applied Math. Nonlinear Sci., 3 (2018), 241-254. doi: 10.21042/AMNS.2018.1.00018
    [29] H. Bulut, T. A. Sulaiman, H. M. Baskonus, New solitary and optical wave structures to the Korteweg-de Vries equation with dual-power law nonlinearity, Opt. Quant. Electron., 48 (2016), 1-14. doi: 10.1007/s11082-015-0274-3
    [30] H. Bulut, T. A. Sulaiman, H. M. Baskonus, et al., New solitary and optical wave structures to the (1+1)-Dimensional combined KdV-mKdV equation, Optik, 135 (2017), 327-336. doi: 10.1016/j.ijleo.2017.01.071
    [31] C. Yan, A Simple Transformation for nonlinear waves, Phys. Lett. A, 22 (1996), 77-84.
    [32] E. W. Weisstein, Concise encyclopedia of mathematics, Secnd Eds., New York, CRC Press, 2002.
    [33] W. Gao, H. F. Ismael, A. M. Husien, et al., Optical soliton solutions of the nonlinear Schrodinger and resonant nonlinear Schrodinger equation with parabolic Law, Applied Sci., 10 (2020), 1-20.
    [34] J. L. G. Guirao, H. M. Baskonus, A. Kumar, et al., Complex soliton solutions to the (3+1)- dimensional B-type Kadomtsev-Petviashvili-Boussinesq equation, Symmetry, 12 (2020), 1-17.
    [35] W. Gao, G. Yel, H. M. Baskonus, et al., Complex solitons in the conformable (2+1)-dimensional Ablowitz-Kaup-Newell-Segur equation, Aims Math., 5 (2020), 507-521. doi: 10.3934/math.2020034
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(6363) PDF downloads(602) Cited by(76)

Article outline

Figures and Tables

Figures(10)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog