期刊
WAVES IN RANDOM AND COMPLEX MEDIA
卷 26, 期 4, 页码 444-457出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/17455030.2016.1166289
关键词
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资金
- Fundamental Research Funds for the Central Universities [2015QNA53]
- Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Mines
- China Postdoctoral Science Foundation [2015M570498]
- Natural Sciences Foundation of China [11301527]
In this paper, a (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko (gBK) equation is investigated, which can be used to describe the interaction of a Riemann wave propagating along y-axis and a long wave propagating along x-axis. The complete integrability of the gBK equation is systematically presented. By employing Bell's polynomials, a lucid and systematic approach is proposed to systematically study its bilinear formalism, bilinear Backlund transformations, Lax pairs, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic wave solutions and soliton solutions of the gBK equation are derived. Finally, an asymptotic relation between the periodic wave solutions and soliton solutions are strictly established under a certain limit condition.
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