Journal
APPLIED MATHEMATICAL MODELLING
Volume 39, Issue 12, Pages 3221-3226Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2014.10.046
Keywords
Bell polynomials; Bell-polynomial-typed Backlund transformation; Two-dimensional Korteweg-de Vries model; Bilinear method; Symbolic computation
Funding
- National Natural Science Foundation of China [61308018]
- China Postdoctoral Science Foundation [2014T70031]
- Fundamental Research Funds for the Central Universities of China [2014RC019, 2015JBM111]
- State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiao Tong University [RCS2012ZT004]
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With symbolic computation, Bell-polynomial scheme and bilinear method are applied to a two-dimensional Korteweg-de Vries (KdV) model, which is firstly proposed with Lax pair generating technique. Bell-polynomial expression with one auxiliary independent variable is derived and transformed into bilinear form. According to the coupled two-field conditions between the primary and replica fields, Bell-polynomial-typed Backlund transformations (BTs) are constructed and converted into the bilinear ones. Finally, soliton solutions of the two-dimensional KdV model are obtained (via solving the bilinear representation and BT, respectively) and compared. Such associated integrable properties as bilinear representation, BT (especially auxiliary-independent-variable-involved Bell-polynomial-typed ones constructed in this paper) and soliton solutions (especially the multi-soliton ones) may be useful for further study on other two-dimensional KdV and KdV-typed models. (C) 2014 Elsevier Inc. All rights reserved.
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