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On the integrability of the (1+1)‐dimensional and (2+1)‐dimensional Ito equations
Author(s) -
Wang YunHu
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3056
Subject(s) - mathematics , bilinear interpolation , bilinear transform , bilinear form , transformation (genetics) , bell polynomials , soliton , one dimensional space , symbolic computation , symmetric bilinear form , lax pair , computation , pure mathematics , algebra over a field , mathematical physics , nonlinear system , mathematical analysis , integrable system , algorithm , quantum mechanics , computer science , physics , digital filter , biochemistry , statistics , chemistry , filter (signal processing) , computer vision , gene
Under investigation in this paper are the (1+1)‐dimensional and (2+1)‐dimensional Ito equations. With the help of the Bell polynomials method, Hirota bilinear method and symbolic computation, the bilinear representations, N ‐soliton solutions, bilinear Bäcklund transformations and Lax pairs of these two equations are obtained, respectively. In particular, we obtain a new bilinear form and N ‐soliton solutions of the (2+1)‐dimensional Ito equation. The bilinear Bäcklund transformation and Lax pair of the (2+1)‐dimensional Ito equation are also obtained for the first time. Copyright © 2014 John Wiley & Sons, Ltd.
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