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

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

E-mail Address: lijb@zjnu.cn

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and

Fengjuan Chen

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

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https://doi.org/10.1142/S0218127416500115Cited by:2 (Source: Crossref)

Abstract

In this paper, we consider a modulated equation in a discrete nonlinear electrical transmission line. This model is an integrable planar dynamical system having three singular straight lines. By using the theory of singular systems to investigate the dynamical behavior for this system, we obtain bifurcations of phase portraits under different parameter conditions. Corresponding to some special level curves, we derive exact explicit parametric representations of solutions (including smooth solitary wave solutions, peakons, compactons, periodic cusp wave solutions) under different parameter conditions.

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

Keywords:

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