Finding New Types of Peakon Solutions for FitzHugh-Nagumo Equation by an Analytical Technique

ZOU Li; WANG Zhen; LIANG Hui; ZONG Zhi; ZOU Hao

doi:10.3879/j.issn.1000-0887.2013.11.003

Volume 34 Issue 11

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ZOU Li, WANG Zhen, LIANG Hui, ZONG Zhi, ZOU Hao. Finding New Types of Peakon Solutions for FitzHugh-Nagumo Equation by an Analytical Technique[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1141-1149. doi: 10.3879/j.issn.1000-0887.2013.11.003

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Finding New Types of Peakon Solutions for FitzHugh-Nagumo Equation by an Analytical Technique

doi: 10.3879/j.issn.1000-0887.2013.11.003

ZOU Li^1,2,
WANG Zhen³,
LIANG Hui^1,4,
ZONG Zhi^1,4,
ZOU Hao^1,2

¹State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian, Liaoning 116085, P.R.China;²School of Aeronautics and Astronautics, Dalian University of Technology,Dalian, Liaoning 116085, P.R.China;³School of Mathematics, Dalian University of Technology, Dalian, Liaoning 116085, P.R.China;⁴School of Naval Architecture, Dalian University of Technology, Dalian, Liaoning 116085, P.R.China

Funds: The National Basic Research Program of China (973 Program)（2010CB832704； 2013CB036101）;The National Natural Science Foundation of China（51109031； 11072053； 51009022； 51221961； 51239002）

Received Date: 2013-06-14
Rev Recd Date: 2013-08-19
Publish Date: 2013-11-15

Abstract

Abstract

The FitzHugh-Nagumo equation was studied with an approximate analytical method: the differential transform method. Peakon soliton solutions to this equation were presented. As a result, more new types of peakon solutions were obtained. The convergence region and rate of the differential transform method were also analyzed. The differential transform method was successfully combined with the Padé approximation technique, to construct an explicit, totally analytical and uniformly valid peakon soliton solution to FitzHugh-Nagumo equation. The main idea was to limit the boundary conditions while let the derivative at the crest of the solitary wave not exist but the solitary waves of the derivative exist at both sides. The obtained results show that the differential transform method can avoid the limitation of perturbation under conditions of very small parameters. The present method provides a powerful and effective mathematical tool to obtain new types of precise peakon solutions for FitzHugh-Nagumo equation.
- FitzHugh-Nagumo equation,
- peakon solution,
- differential transform method,
- Padé approximation,
- convergence region and rate

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References(18)

References

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