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

Wei Gao; Mine Senel; Gulnur Yel; Haci Mehmet Baskonus; Bilgin Senel; Wei Gao; Mine Senel; Gulnur Yel; Haci Mehmet Baskonus; Bilgin Senel

doi:10.3934/math.2020125

AIMS Mathematics

2020, Volume 5, Issue 3: 1881-1892. doi: 10.3934/math.2020125

Previous Article Next Article

Research article Special Issues

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

1.
School of Information Science and Technology, Yunnan Normal University, Yunnan, China
2.
Mugla Sitki Kocman University, Fethiye Faculty of Business Administration, Mugla, Turkey
3.
Faculty of Educational Sciences, Final International University, Kyrenia, Mersin 10, Turkey
4.
Harran University, Faculty of Education, Sanliurfa, Turkey

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.
- nonlinear electrical transmission line equation,
- SGEM,
- exponential results with complex,
- contour graphs,
- density surfaces
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:

Abstract

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.

References

[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

Your name:*

Email:*
© 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)