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Bilinear Bäcklund transformation, N ‐soliton, and infinite conservation laws for Lax–Kadomtsev–Petviashvili and generalized Korteweg–de Vries equations
Author(s) -
Wael Shrouk,
Seadawy Aly R.,
Moawad Salah M.,
ElKalaawy Omar H.
Publication year - 2021
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.7516
Subject(s) - mathematics , conservation law , lax pair , bell polynomials , bilinear interpolation , transformation (genetics) , bilinear form , korteweg–de vries equation , soliton , mathematical physics , bilinear transform , pure mathematics , integrable system , mathematical analysis , nonlinear system , physics , quantum mechanics , biochemistry , statistics , chemistry , gene , digital filter , filter (signal processing) , computer science , computer vision
In this paper, we obtain the bilinear form for the Lax–Kadomtsev–Petviashvili (Lax–KP) and the generalized (3 + 1)‐dimensional Korteweg–de Vries equations based on the binary Bell polynomials. Accordingly, N ‐soliton solutions, bilinear Bäcklund transformation, Lax pair, and infinite conservation laws will be constructed to Lax–KP and the generalized (2 + 1)‐dimensional Korteweg–de Vries equation( 2 + 1 ) G − K d V . At the same time, we get another bilinear Bäcklund transformation. Finally, exact solutions were obtained by using the exchange formulas for Hirota's bilinear operators.