Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 31, Issue -, Pages 388-408Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2016.01.019
Keywords
The (2+1)-dimensional Boussinesq equation; Bell's polynomials; Backlund transformation; Infinite conservation laws; Periodic wave solution; Soliton solution
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Funding
- Fundamental Research Funds for the Central Universities [2015XKQY14]
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Under investigation in this paper is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the water wave interaction. By using Bell polynomials, a lucid and systematic approach is proposed to systematically study the integrability of the equation, including its bilinear representation, soliton solutions, periodic wave solutions, Backlund transformation and Lax pairs, respectively. Furthermore, by virtue of its Lax equations, the infinite conservation laws of the equation are also derived with the recursion formulas. Finally, the asymptotic behavior of periodic wave solutions is shown with a limiting procedure. (C) 2016 Elsevier Ltd. All rights reserved.
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