Abstract.
This paper retrieves soliton solutions to an equation in nonlinear electrical transmission lines using the semi-inverse variational principle method (SIVPM), the \(\exp(-\Omega(\xi))\) -expansion method (EEM) and the improved \(\tan(\phi/2)\) -expansion method (ITEM), with the aid of the symbolic computation package Maple. As a result, the SIVPM, EEM and ITEM methods are successfully employed and some new exact solitary wave solutions are acquired in terms of kink-singular soliton solution, hyperbolic solution, trigonometric solution, dark and bright soliton solutions. All solutions have been verified back into their corresponding equations with the aid of the Maple package program. We depicted the physical explanation of the extracted solutions with the choice of different parameters by plotting some 2D and 3D illustrations. Finally, we show that the used methods are robust and more efficient than other methods. More importantly, the solutions found in this work can have significant applications in telecommunication systems where solitons are used to codify data.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Tala-Tebue, D.C. Tsobgni-Fozap, A. Kenfack-Jiotsa, T.C. Kofane, Eur. Phys. J. Plus 129, 136 (2014)
W.S. Duan, Europhys. Lett. 66, 192 (2004)
A. Sardar, S.M. Husnine, S.T.R. Rizvi, M. Younis, K. Ali, Nonlinear Dyn. 82, 1317 (2015)
J. Yu, W.J. Zhang, X.M. Gao, Chaos, Solitons Fractals 33, 1307 (2007)
H.-L. Zhen, B. Tian, H. Zhong, Y. Jiang, Comput. Math. Appl. 68, 579 (2014)
E.V. Krishnan, A. Biswas, Phys. Wave Phenom. 18, 256 (2010)
N. Naranmandula, K.X. Wang, Phys. Lett. A 336, 112 (2005)
K. Nozaki, N. Bekki, Phys. Rev. Lett. 50, 1226 (1983)
M. Panthee, M. Scialom, Stud. Appl. Math. 124, 229 (2010)
M. Ekici, M. Mirzazadeh, A. Sonmezoglu, Q. Zhou, H. Triki, M. Zaka Ullah, S.P. Moshokoa, A. Biswas, Optik 131, 964 (2017)
J. Manafian, M. Lakestani, Eur. Phys. J. Plus 130, 61 (2015)
J. Manafian, Eur. Phys. J. Plus 130, 255 (2015)
A.H. Arnous, M.Z.U. Seithuti, P. Moshokoa, Q. Zhou, H. Triki, M. Mirzazadeh, A. Biswas, Nonlinear Dyn. 88, 1891 (2017)
Q. Zhou, M. Ekici, A. Sonmezoglu, J. Manafian, S. Khaleghizadeh, M. Mirzazadeh, Optik 127, 12085 (2016)
M. Ekici, Q. Zhou, A. Sonmezoglu, J. Manafian, M. Mirzazadeh, Optik 130, 378 (2017)
J. Manafian, Optik 127, 4222 (2016)
J. Manafian, M. Lakestani, Opt. Quantum Electron. 48, 1 (2016)
J. Manafian, M. Lakestani, Optik 127, 5543 (2016)
J. Manafian, Opt. Quantum Electron. 49, 17 (2017)
J. Manafian, M. Lakestani, Pramana - J. Phys. 130, 31 (2015)
C.T. Sindi, J. Manafian, Math. Methods Appl. Sci. 40, 4350 (2017)
R.F. Zinati, J. Manafian, Eur. Phys. J. Plus 132, 155 (2017)
H.M. Baskonus, AIP Conf. Proc. 1798, 020018 (2017)
H.M. Baskonus, H. Bulut, Waves Random Complex Media 26, 201 (2016)
Q. Zhou, Waves Random Complex Media 25, 52 (2016)
W.X. Ma, B. Fuchssteiner, Int. J. Non-Linear Mech. 31, 329 (1996)
W.X. Ma, J.-H. Lee, Chaos, Solitons Fractals 42, 1356 (2009)
W.X. Ma, T. Huang, Y. Zhang, Phys. Scr. 82, 065003 (2010)
W.X. Ma, Z. Zhu, Appl. Math. Comput. 218, 11871 (2012)
W.X. Ma, Sci. China Math. 55, 1769 (2012)
M. Mirzazadeh, M. Eslami, Eur. Phys. J. Plus 128, 132 (2013)
F. Tchier, A. Yusuf, A.I. Aliyu, M. Inc, Superlattices Microstruct. 107, 320 (2017)
A.M. Wazwaz, Nonlinear Dyn. 87, 1685 (2017)
A.M. Wazwaz, S.A. El-Tantawy, Nonlinear Dyn. 87, 2457 (2017)
D. Talati, A.M. Wazwaz, Nonlinear Dyn. 87, 1111 (2017)
A.M. Wazwaz, Nonlinear Dyn. 88, 1727 (2017)
F. Yu, L. Feng, L. Li, Nonlinear Dyn. 88, 1257 (2017)
X. Geng, Y. Lv, Nonlinear Dyn. 69, 1621 (2012)
L.-L. Wen, H.-Q. Zhang, Nonlinear Dyn. 84, 863 (2016)
X. Lü, B. Tian, H.-Q. Zhang, T. Xu, H. Li, Nonlinear Dyn. 67, 2279 (2012)
L. Na, Nonlinear Dyn. 82, 311 (2015)
J.H. He, Int. J. Mod. Phys. B 20, 1141 (2006)
R. Kohl, D. Milovic, E. Zerrad, A. Biswas, J. Infrared Millim. Terahertz Waves 30, 526 (2009)
J. Zhang, Comput. Math. Appl. 54, 1043 (2007)
J. Manafian, M. Lakestani, Optik 127, 9603 (2016)
J. Manafian, M. Lakestani, A. Bekir, J. Porous Media 19, 975 (2016)
K. Khan, M.A. Akbar, Int. J. Dyn. Syst. Differ. Equ. 5, 72 (2014)
S.M. Rayhanul Islam, K. Khan, M.A. Akbar, Springer Plus 4, 124 (2015)
M.G. Hafez, Md.N. Alam, M.A. Akbar, J. King Saud Univ.-Sci. 27, 105 (2015)
M.G. Hafez, Md. Nur Alam, M.A. Akbar, World Appl. Sci. J. 32, 2150 (2014)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Manafian, J., Lakestani, M. New exact solutions for a discrete electrical lattice using the analytical methods. Eur. Phys. J. Plus 133, 119 (2018). https://doi.org/10.1140/epjp/i2018-11939-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2018-11939-6