期刊
NONLINEAR DYNAMICS
卷 88, 期 3, 页码 2265-2279出版社
SPRINGER
DOI: 10.1007/s11071-017-3375-7
关键词
A generalized (3+1)-dimensional variable-coefficient BKP equation; Bell's polynomials; Solitary wave solutions; Periodic wave solutions; Traveling wave solutions
资金
- Fundamental Research Fund for Talents Cultivation Project of the China University of Mining and Technology [YC150003]
Under investigation in this paper is a generalized (3 + 1)-dimensional variable-coefficient BKP equation, which can be used to describe the propagation of nonlinear waves in fluid mechanics and other fields. With the aid of binary Bell's polynomials, an effective and straightforward method is presented to explicitly construct its bilinear representation with an auxiliary variable. Based on the bilinear formalism, the soliton solutions and multi-periodic wave solutions are well constructed. Furthermore, the tanh method and the tan method are employed to construct more traveling wave solutions of the equation. Finally, the asymptotic properties of the multi-periodic wave solutions are systematically analyzed to reveal the connection between periodic wave solutions and soliton solutions. It is interesting that the periodic waves tend to solitary waves under a limiting procedure. Our results can be used to enrich the dynamical behavior of higher-dimensional nonlinear wave fields.
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