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“…(1), (2), and (3). (14), (23), and (29)] has generated the Bell-polynomial-typed Bäcklund transformations [see Eqs. (11), (21), and (27)], which can be cast into the Hirota bilinear equations.…”

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“…(1), (2), and (3). (14), (23), and (29)] has generated the Bell-polynomial-typed Bäcklund transformations [see Eqs. (11), (21), and (27)], which can be cast into the Hirota bilinear equations.…”

“…In the published literatures, some NLEEs have been investigated with the Bell-polynomial scheme, e.g., the Burgers-Hopf hierarchy, potential Kortewegde Vries, modified Korteweg-de Vries, potential Sawada-Kotera, sine-Gordon, Ablowitz-Kaup-Newell-Segur system, and Boussinesq equations. II, and then perform the Bell-polynomial manipulations on three nonlinear models: the (1+1)-dimensional shallow water wave model (SWWM), 3,4 Boiti-Leon-Manna-Pempinelli model (BLMPM), 14,15 and (2+1)-dimensional higher-order dispersive Sawada-Kotera model (2+1dHODSKM). 3,11 Then, both the Bell-polynomial-typed and bilinear BTs can lead to the corresponding Lax pairs.…”

“…Integrabilities of (1) in the Painlevé and Lax senses have been discussed [11]. Besides, for (1), multi-periodic solutions [12], variable-separation solutions [13,14], and soliton-like solutions [15] have been obtained. Conversely, integrable versions of the NLEEs usually have the soliton solutions [16][17][18][19][20].…”

“…A set of solitary-like solutions for Eq. (2) were acquired by means of a symbolic-computation-based method [40,41]. In [42], the generalized dromion solutions for Eq.…”