Abstract.
In this work, we use the new Jacobi elliptic function expansion method to find exact soliton solutions for a discrete nonlinear electrical transmission line in (2 + 1) dimension. Several new solutions have been obtained. The solutions found by the current method are of varied types and include hyperbolic and trigonometric solutions, as well as Jacobi elliptic solutions. We show that the existence of these solutions depends on the parameters of the network. Comparisons of our new results with the well-known results are obtained. The solutions found here may be also used in optical fibers to transport information. The method applied here is very simple and concise and can be also applied to other nonlinear partial differential equations.
Similar content being viewed by others
References
E.M.E. Zayed, M.A.M. Abdelaziz, Int. J. Nonlinear Sci. Numer. Simul. 11, 595 (2010)
A.M. Wazwaz, Chaos, Solitons Fractols 25, 55 (2005)
W. Malfliet, Am. J. Phys. 60, 650 (1992)
A.M. Wazwaz, Comput. Math. Appl. 50, 1685 (2005)
A.M. Wazwaz, Appl. Math. Comput. 187, 1131 (2007)
A. Bekir, Phys. Scr. 77, 045008 (2008)
A.M. Wazwaz, Math. Comput. Model. 40, 499 (2004)
G. Tsigaridas, A. Fragos, I. Polyzos, M. Fakis, A. Ioannou, V. Giannetas, P. Persephonis, Chaos, Solitons Fractols 23, 1841 (2005)
M.R. Miura, Bäcklund Transformation (Springer, Berlin, 1978)
C. Rogers, W.F. Shadwick, Bäcklund Transformations and their Applications (NewYork, Academic Press, 1982)
A.A. Suzo, Phys. Lett. A. 335, 88 (2005)
Z.S. Yersultanova, M. Zhassybayeva, K. Yesmakhanova, G. Nugmanova, R. Myrzakulov, Int. J. Geom. Methods Mod. Phys. 13, 1550134 (2016)
R.S. Banerjee, Phys. Scr. 57, 598 (1998)
Zhenya Yan, MM Res. Prep. 22, 294 (2003)
D. Mehdi, S. Fatemeh, Phys. Scr. 75, 778 (2007)
M.M. Khader, S. Kumar, S. Abbasbandy, Chin. Phys. B 22, 110201 (2013)
J.H. He, Phys. Scr. 76, 680 (2007)
V.O. Vakhnenko, E.J. Parkes, A.J. Morrison, Chaos, Solitons Fractols 17, 683 (2003)
M. Wang, X. Li, J. Zhang, Phys. Lett. A 372, 417 (2008)
S. Zhang, J.L. Tong, W. Wang, Phys. Lett. A 372, 2254 (2008)
E.M.E. Zayed, K.A. Gepreel, J. Math. Phys. 50, 013502 (2009)
E.M.E. Zayed, J. Appl. Math. Comput. 30, 89 (2009)
R. Hirota, Phys. Rev. Lett. 27, 1192 (1971)
J. Hietarinta, Introduction to the Hirota Bilinear Method, in Lecture Notes in Physics (Springer-Verlag, 2004)
J. Hietarinta, Phys. AUC 15, 31 (2005)
E.M.E. Zayed, M.A.M. Abdelaziz, Appl. Math. Comput. 218, 2259 (2011)
M.B. Laila Assas, J. Comput. Appl. Math. 233, 97 (2009)
Z. Xin-Wei, J. Phys. Conf. Ser. 96, 012063 (2008)
A.J.M. Jawad, M.D. Petkovic, A. Biswas, Appl. Math. Comput. 217, 869 (2010)
E.M.E. Zayed, Appl. Math. Comput. 218, 3962 (2011)
E.M.E. Zayed, S.A. Hoda Ibrahim, Chin. Phys. Lett. 29, 060201 (2012)
E. Tala-Tebue, Z.I. Djoufack, E. Fendzi-Donfack, A. Kenfack-Jiotsa, T.C. Kofane, Optik 127, 11124 (2016)
E. Aksoy, M. Kaplan, A. Bekir, Waves Random Complex Media 26, 142 (2016)
J. Manafian, J. Jalali, A. Ranjbaran, Opt. Quantum Electron. 49, 1 (2017)
E.M.E. Zayed, M.S. Ayad, A.E.A. Khaled, Opt. Quantum Electron. 50, 96 (2018)
H.C. MA, Z.P. Zhang, A.P. Deng, Acta Math. Appl. Sin. 28, 409 (2012)
E.M.E. Zayed, K.A.E. Alurrfi, Chaos, Solitons Fractols 78, 148 (2015)
E. Tala-Tebue, D.C. Tsobgni-Fozap, A. Kenfack-Jiotsa, T.C. Kofane, Eur. Phys. J. Plus 129, 136 (2014)
L. Huibin, W. Kelin, J. Phys. A: Math. Gen. 23, 4097 (1990)
S. Liu, Z. Fu, S. Liu, Q. Zhao, Phys. Lett. A 289, 69 (2001)
S. Lai, X. Lv, M. Shuai, Math. Comput. Model. 49, 369 (2009)
A.G. Khaled, Adv. Differ. Equ. 286, 1 (2014)
E.M.E. Zayed, K.A.E. Alurrfi, Ric. Mat. 65, 235 (2016)
J.A. Giannini, R.I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990)
J.P. Hamaide, P. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991)
Y.S. Kivshar, M. Haelterman, P. Emplit, J.P. Hamaide, Opt. Lett. 19, 19 (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tala-Tebue, E., Zayed, E.M.E. New Jacobi elliptic function solutions, solitons and other solutions for the (2 + 1)-dimensional nonlinear electrical transmission line equation. Eur. Phys. J. Plus 133, 314 (2018). https://doi.org/10.1140/epjp/i2018-12118-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2018-12118-7