Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis
In this paper, based on the dynamical system method, we obtain the exact parametric expressions of the travelling wave solutions of the Wu–Zhang system. Our approach is much different from the existing literature studies on the Wu–Zhang system. Moreover, we also study the fractional derivative of th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/2845841 |
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| _version_ | 1832566001765449728 |
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| author | Hang Zheng Yonghui Xia Yuzhen Bai Guo Lei |
| author_facet | Hang Zheng Yonghui Xia Yuzhen Bai Guo Lei |
| author_sort | Hang Zheng |
| collection | DOAJ |
| description | In this paper, based on the dynamical system method, we obtain the exact parametric expressions of the travelling wave solutions of the Wu–Zhang system. Our approach is much different from the existing literature studies on the Wu–Zhang system. Moreover, we also study the fractional derivative of the Wu–Zhang system. Finally, by comparison between the integer-order Wu–Zhang system and the fractional-order Wu–Zhang system, we see that the phase portrait, nonzero equilibrium points, and the corresponding exact travelling wave solutions all depend on the derivative order α. Phase portraits and simulations are given to show the validity of the obtained solutions. |
| format | Article |
| id | doaj-art-755f539179ee4c618ef9bfbf40ff2a8a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-755f539179ee4c618ef9bfbf40ff2a8a2025-02-03T01:05:23ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/28458412845841Travelling Wave Solutions of Wu–Zhang System via Dynamic AnalysisHang Zheng0Yonghui Xia1Yuzhen Bai2Guo Lei3Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaDepartment of Mathematics and Computer, Wuyi University, Wuyishan 354300, ChinaIn this paper, based on the dynamical system method, we obtain the exact parametric expressions of the travelling wave solutions of the Wu–Zhang system. Our approach is much different from the existing literature studies on the Wu–Zhang system. Moreover, we also study the fractional derivative of the Wu–Zhang system. Finally, by comparison between the integer-order Wu–Zhang system and the fractional-order Wu–Zhang system, we see that the phase portrait, nonzero equilibrium points, and the corresponding exact travelling wave solutions all depend on the derivative order α. Phase portraits and simulations are given to show the validity of the obtained solutions.http://dx.doi.org/10.1155/2020/2845841 |
| spellingShingle | Hang Zheng Yonghui Xia Yuzhen Bai Guo Lei Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis Discrete Dynamics in Nature and Society |
| title | Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis |
| title_full | Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis |
| title_fullStr | Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis |
| title_full_unstemmed | Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis |
| title_short | Travelling Wave Solutions of Wu–Zhang System via Dynamic Analysis |
| title_sort | travelling wave solutions of wu zhang system via dynamic analysis |
| url | http://dx.doi.org/10.1155/2020/2845841 |
| work_keys_str_mv | AT hangzheng travellingwavesolutionsofwuzhangsystemviadynamicanalysis AT yonghuixia travellingwavesolutionsofwuzhangsystemviadynamicanalysis AT yuzhenbai travellingwavesolutionsofwuzhangsystemviadynamicanalysis AT guolei travellingwavesolutionsofwuzhangsystemviadynamicanalysis |