Qualitative and quantitative analysis of nonlinear dynamics by the complete discrimination system for polynomial method

Yue Kai, Shuangqing Chen, Bailin Zheng, Kai Zhang, Nan Yang and Wenlong Xu

Chaos, Solitons & Fractals, 2020, vol. 141, issue C

Abstract: We show that via the complete discrimination system for polynomial method, the bifurcation, critical condition and topological properties of the nonlinear dynamics can be seen very easily. Concrete example of perturbed Gardner’s equation with high order dispersion also verifies our conclusion. The results indicate that the complete discrimination system for polynomial method can not only be used to get quantitative results such as the classification of the traveling wave solutions, but also to conduct qualitative analysis for the nonlinear differential equations.

Keywords: Complete discrimination system for polynomial method; Nonlinear dynamics; Bifurcation; Qualitative analysis; Quantitative analysis; Perturbed Gardner’s equation with high order dispersion (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307104

DOI: 10.1016/j.chaos.2020.110314

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