期刊
WAVES IN RANDOM AND COMPLEX MEDIA
卷 29, 期 2, 页码 247-263出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/17455030.2018.1428382
关键词
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资金
- Ministry of Industry and Information Technology of China [[2016] 22]
- Research and Practice of Educational Reform for Graduate students in China University of Mining and Technology [YJSJG_2017_049]
- 'Qinglan Engineering project' of Jiangsu Universities
- National Natural Science Foundation of China [11301527, 51522902]
- Fundamental Research Funds for the Central Universities [DUT17ZD233]
- China Postdoctoral Science Foundations [2015M570498, 2017T100413]
Under investigation in this paper is a fifth-order Korteweg-de Vries (fKdV) equation, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the binary Bell polynomials, a lucid and systematic approach is proposed to systematically study its bilinear representation, bilinear Backlund transformations and Lax pairs with explicit formulas, respectively. These results can be reduced to the ones of several integrable equations such as Sawada-Kotera equation, Caudrey-Dodd-Gibbon equation, Lax equation, Kaup-Kuperschmidt equation and Ito equation, etc. Furthermore, the N-solitary wave solutions formula and quasi-periodic wave solutions are obtained by using bilinear form of the fKdV equation. Finally, the relation between the periodic wave solution and solitary wave solution is rigorously established.
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