Journal
NONLINEAR DYNAMICS
Volume 77, Issue 1-2, Pages 135-143Publisher
SPRINGER
DOI: 10.1007/s11071-014-1279-3
Keywords
Bogoyavlensky-Konoplechenko model; Bell-polynomial manipulation; N-soliton solution; Bilinear Backlund transformation; Wronskian solution; Symbolic computation
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Funding
- National Natural Science Foundation of China [61308018, 11101421]
- China Postdoctoral Science Foundation [2012M520154]
- Fundamental Research Funds for the Central Universities of China [2013JBM088]
- Project of State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiao Tong University [RCS2012ZT004]
- Special Foundation for Young Scientists of Institute of Remote Sensing and Digital Earth of Chinese Academy of Sciences [Y1S01500CX]
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With symbolic computation, this paper investigates some integrable properties of a two-dimensional generalization of the Korteweg-de Vries equation, i.e., the Bogoyavlensky-Konoplechenko model, which can govern the interaction of a Riemann wave propagating along the -axis and a long wave propagating along the -axis. Within the framework of Bell-polynomial manipulations, Bell-polynomial expressions are firstly given, which then are cast into bilinear forms. The -soliton solutions in the form of an th-order polynomial in the exponentials and in terms of the Wronskian determinant are, respectively, constructed with the Hirota bilinear method and Wronskian technique. Bilinear Backlund transformation is also derived with the achievement of a family of explicit solutions.
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