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

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

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Fengjuan Chen

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

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https://doi.org/10.1142/S0218127415500455Cited by:5 (Source: Crossref)

Abstract

In this paper, we consider a model which is the 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 and investigating the dynamical behavior, we obtain bifurcations of the phase portraits of the system under different parameter conditions. Corresponding to some special level curves, we derive possible exact explicit parametric representations of solutions (including smooth solitary wave and periodic wave solutions, periodic cusp wave solutions) under different parameter conditions.

This research was partially supported by the National Natural Science Foundation of China (11471289, 11171309, 11162020).

Keywords:

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