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Bell polynomial approach to an extended Korteweg–de Vries equation
Author(s) -
Wang Hui,
Xia Tiecheng
Publication year - 2013
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.2908
Subject(s) - korteweg–de vries equation , mathematics , lax pair , soliton , bilinear interpolation , conservation law , bilinear form , quasiperiodic function , riemann hypothesis , mathematical physics , polynomial , covariant transformation , mathematical analysis , type (biology) , transformation (genetics) , integrable system , nonlinear system , physics , quantum mechanics , ecology , statistics , biology , biochemistry , chemistry , gene
Under investigation in this paper is an extended Korteweg–de Vries equation. Via Bell polynomial approach and symbolic computation, this equation is transformed into two kinds of bilinear equations by choosing different coefficients, namely KdV–SK‐type equation and KdV–Lax‐type equation. On the one hand, N ‐soliton solutions, bilinear Bäcklund transformation, Lax pair, Darboux covariant Lax pair, and infinite conservation laws of the KdV–Lax‐type equation are constructed. On the other hand, on the basis of Hirota bilinear method and Riemann theta function, quasiperiodic wave solution of the KdV–SK‐type equation is also presented, and the exact relation between the one periodic wave solution and the one soliton solution is established. It is rigorously shown that the one periodic wave solution tend to the one soliton solution under a small amplitude limit. Copyright © 2013 John Wiley & Sons, Ltd.