PapersNo Access

Exact Solutions and Bifurcations of a Modulated Equation in a Discrete Nonlinear Electrical Transmission Line (I)

Jibin Li

Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

Department of Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China

Search for more papers by this author

and

Lin Jiang

Department of Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S0218127415500169Cited by:6 (Source: Crossref)

Abstract

In this paper, we consider a model which is a modulated equation in a discrete nonlinear electrical transmission line. By investigating the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we derive all explicit exact parametric representations of solutions (including smooth solitary wave solutions, smooth periodic wave solutions, peakons, compactons, periodic cusp wave solutions, etc.) under different parameter conditions.

This research was partially supported by the National Natural Science Foundation of China (11471289, 11162020).

Keywords:

References

P. F. Byrd and M. D. Fridman , Handbook of Elliptic Integrals for Engineers and Scientists ( Springer , Berlin , 1971 ) . Crossref, Google Scholar
F. Kenmogne and D. Yemélé , Chaos Solit. Fract. 45 , 21 ( 2012 ) . Crossref, Web of Science, Google Scholar
Kenmogne, F., Ndombou, G. B., Yem'elé, D. & Fomethe, A. [2015] "Nonlinear supratransmission in a discrete nonlinear electrical transmission line: Modulated gap peak solitons," Chaos Solit. Fract., to appear . Google Scholar
J. Li and G. Chen , Int. J. Bifurcation and Chaos 17 , 4049 ( 2007 ) . Link, Web of Science, Google Scholar
J. Li , Singular Nonlinear Traveling Wave Equations: Bifurcations and Exact Solutions ( Science , Beijing , 2013 ) . Google Scholar
J. Li and Z. Qiao , J. Math. Phys. 54 , 123501-1 ( 2013 ) . Crossref, Web of Science, Google Scholar
D. Yemélé and F. Kenmogne , Phys. Lett. A 373 , 3801 ( 2009 ) . Crossref, Web of Science, Google Scholar