A note on exact complex travelling wave solutions for (2+1)-dimensional B-type Kadomtsev–Petviashvili equation

Bäcklund transformation and multi-soliton solutions for the (3+1)-dimensional BKP equation with Bell polynomials and symbolic computation

“…Combining P-polynomials (14) with formula (7), it is easy to obtain the following bilinear form of the BKP Eq. (1)…”

“…Methods to construct soliton solutions have been developed, such as inverse scattering method, Hirota's bilinear form method, tanh method, F-expansion method, expfunction method, Bäcklund transformation method, L. Na (B) Business School, Shandong University of Political Science and Law, Jinan 250014, People's Republic of China e-mail: sna0531@126.com Lie symmetry method, Darboux transformation, binary Kudryashov method, three-wave method [1][2][3][4][5][6][7][8][9][10][11][12] and so on. Among them, three-wave method can be used to construct the soliton solutions directly for such NLEEs as the KP equation, Boussinesq equation and SawadaKotera equation [13][14][15].…”

New Localized Structure for (2+1) Dimensional Boussinesq-Kadomtsev-Petviashvili Equation

“…The authors in [20] have studied its various exact solutions by using the bifurcation theory of dynamical systems. Zhang and Cheng's groups have also constructed its exact solutions by the G G -expansion method and the first integral method [21,22]. Recently, Akinyemi et al have obtained numerous exact solutions of generalized (B-KP)-like equations with four different forms by using sub-equation method [23].…”

Lump solutions for the dimensionally reduced variable coefficient B-type Kadomtsev-Petviashvili equation

“…As a kind of rational function solutions, lump solutions, which localize in all directions in the space, have many applications to nonlinear partial differential equations. Recently, a hot topic is the KP-type equations [11][12][13][14], such as the (2+1)-dimensional B-type KP equation, the (3+1)-dimensional B-type KP equation, which can be transformed into a generalized bilinear equation. Multi-component and higher-order extensions of lump solutions exhibit diverse soliton phenomena, particularly the (3+1)-dimensional case always leads to multiple wave solutions and lump solutions.…”