Continuous limit, various exact solutions, kink soliton resonant phenomena and dynamical behaviors for a discrete Burgers equation
The Burgers equation can describe some phenomena such as turbulence, shock wave and traffic flow dynamics problems. Under consideration in this paper is a discrete Burgers equation, which can be viewed as the discrete counterpart of Burgers equation. Firstly, we correspond this discrete equation to...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-05-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722001711 |
| _version_ | 1811280268282036224 |
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| author | Ting Zhang Xiao-Yong Wen Zhe Lin |
| author_facet | Ting Zhang Xiao-Yong Wen Zhe Lin |
| author_sort | Ting Zhang |
| collection | DOAJ |
| description | The Burgers equation can describe some phenomena such as turbulence, shock wave and traffic flow dynamics problems. Under consideration in this paper is a discrete Burgers equation, which can be viewed as the discrete counterpart of Burgers equation. Firstly, we correspond this discrete equation to the famous continuous Burgers equation under the continuous limit. Secondly, based on its 2 × 2 matrix linear spectral problem, we construct the discrete generalized (m,N−m)-fold Darboux transformation (DT) to derive various exact solutions covering kink soliton, rational solutions, semi-rational solutions as well as their mixed superposition solutions. Furthermore, we discuss kink multi-soliton resonant phenomena through the graphics analysis and use asymptotic analysis technique to investigate the limit states of various exact solutions. Finally, the dynamical evolutions of kink soliton solutions are studied through numerical simulations. The results obtained in this paper may be useful for exploring physical phenomena governed by Burgers equation. |
| first_indexed | 2024-04-13T01:11:41Z |
| format | Article |
| id | doaj.art-f747cedf078b4b2d9bc4135584301eb8 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-13T01:11:41Z |
| publishDate | 2022-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-f747cedf078b4b2d9bc4135584301eb82022-12-22T03:09:09ZengElsevierResults in Physics2211-37972022-05-0136105409Continuous limit, various exact solutions, kink soliton resonant phenomena and dynamical behaviors for a discrete Burgers equationTing Zhang0Xiao-Yong Wen1Zhe Lin2School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, ChinaCorresponding author.; School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, ChinaSchool of Applied Science, Beijing Information Science and Technology University, Beijing 100192, ChinaThe Burgers equation can describe some phenomena such as turbulence, shock wave and traffic flow dynamics problems. Under consideration in this paper is a discrete Burgers equation, which can be viewed as the discrete counterpart of Burgers equation. Firstly, we correspond this discrete equation to the famous continuous Burgers equation under the continuous limit. Secondly, based on its 2 × 2 matrix linear spectral problem, we construct the discrete generalized (m,N−m)-fold Darboux transformation (DT) to derive various exact solutions covering kink soliton, rational solutions, semi-rational solutions as well as their mixed superposition solutions. Furthermore, we discuss kink multi-soliton resonant phenomena through the graphics analysis and use asymptotic analysis technique to investigate the limit states of various exact solutions. Finally, the dynamical evolutions of kink soliton solutions are studied through numerical simulations. The results obtained in this paper may be useful for exploring physical phenomena governed by Burgers equation.http://www.sciencedirect.com/science/article/pii/S2211379722001711The discrete Burgers equationContinuous limitDiscrete generalized (m, N – m)-fold DTKink soliton resonanceNumerical simulation |
| spellingShingle | Ting Zhang Xiao-Yong Wen Zhe Lin Continuous limit, various exact solutions, kink soliton resonant phenomena and dynamical behaviors for a discrete Burgers equation Results in Physics The discrete Burgers equation Continuous limit Discrete generalized (m, N – m)-fold DT Kink soliton resonance Numerical simulation |
| title | Continuous limit, various exact solutions, kink soliton resonant phenomena and dynamical behaviors for a discrete Burgers equation |
| title_full | Continuous limit, various exact solutions, kink soliton resonant phenomena and dynamical behaviors for a discrete Burgers equation |
| title_fullStr | Continuous limit, various exact solutions, kink soliton resonant phenomena and dynamical behaviors for a discrete Burgers equation |
| title_full_unstemmed | Continuous limit, various exact solutions, kink soliton resonant phenomena and dynamical behaviors for a discrete Burgers equation |
| title_short | Continuous limit, various exact solutions, kink soliton resonant phenomena and dynamical behaviors for a discrete Burgers equation |
| title_sort | continuous limit various exact solutions kink soliton resonant phenomena and dynamical behaviors for a discrete burgers equation |
| topic | The discrete Burgers equation Continuous limit Discrete generalized (m, N – m)-fold DT Kink soliton resonance Numerical simulation |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722001711 |
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