Explicit exact traveling wave solutions and bifurcations of the generalized combined double sinh–cosh-Gordon equation

Bei Zhang, Yonghui Xia, Wenjing Zhu and Yuzhen Bai

Applied Mathematics and Computation, 2019, vol. 363, issue C, -

Abstract: This paper concerns the qualitative behavior and exact traveling wave solutions of the generalized double combined sinh–cosh-Gordon equation. This equation generalizes sinh-Gordon equation, Liouville equation, Dodd–Bullough–Mikhailov equation, Tzitzeica–Dodd-Bullough equation and Zhiber-Shabat equation as special cases. Thus, this paper presents a unified analysis to find the exact solutions of these known equations. Our results generalize many previous known results (Chen et al., 2009; Fan et al., 2011; Geng et al., 2007; He and Meng, 2017; He et al. 2014; Li and Li 2005; Seadawy et al. 2017; Tang and Huang 2007). We find different kinds of exact solutions such as bright soliton, dark soliton, kink wave, anti-kink wave solutions and periodic wave solutions. Moreover, the explicit expressions of the bounded exact traveling wave solutions are given. Finally, a conclusion ends this paper.

Keywords: Bifurcation; Traveling wave; Sinh–Gordon equation; Periodic wave solution; Solitary wave solution; Kink and anti-kink wave solution (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:363:y:2019:i:c:16

DOI: 10.1016/j.amc.2019.124576

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