Breather wave and lump‐type solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid

Abstract

Under investigation is a new (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. The main results are listed as follows: (i) lump solutions; (ii) interaction solutions between lump wave and solitary waves; (iii) interaction solutions between lump wave and periodic waves; and (iv) breather wave solutions. Furthermore, graphical representation of all solutions is studied and shown in some 3D and contour plots.

Three types of periodic solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation via bilinear neural network method

“…35 After that, more and more solutions are solved of Equation ( 1) such as breather wave, lump-type solutions, and their interaction solutions as well as analytical solutions. 38,39 A general bilinear form to generate different wave structures of solitons for a (3 + 1)-dimensional BLMP equation is studied. 40 As far as we know, periodic-type I-III solutions of the new (3 + 1)-dimensional BLMP equation ( 1) have not been studied.…”

“…The integrability and compatibility conditions of the new (3 + 1)‐dimensional BLMP equation has been studied by the method of Painlevé analysis, at the same time, Hirota's direct method and Painlevé test applied to to solve its multiple soliton and multiple complex soliton solutions 35 . After that, more and more solutions are solved of Equation () such as breather wave, lump‐type solutions, and their interaction solutions as well as analytical solutions 38,39 . A general bilinear form to generate different wave structures of solitons for a (3 + 1)‐dimensional BLMP equation is studied 40 …”

Bäcklund transformation and some different types of N‐soliton solutions to the (3 + 1)‐dimensional generalized nonlinear evolution equation for the shallow‐water waves

“…Several analytical and numerical techniques have been formulated for tackling these types of nonlinear models, including the inverse scattering transform method, 1 the Hirota bilinear method, [2][3][4][5][6][7] Bäcklund transformation method, 8 Darboux transformation method, 9,10 the (G ′ /G)-expansion method, 11 the multiple exp-function method, 12,13 the transformed rational function method, 14,15 and Lie symmetries. 16,17 Many higher dimensional NLEEs may provide more beneficial information, and they always possess more abundant explicit solutions, including lump solutions, [18][19][20][21] lump-type solutions, [22][23][24][25] high-order lump-type solutions, 26 and rogue wave solutions. 27,28 Various exact solutions of some NLEEs were studied, such as the generalized (3 + 1)-dimensional Kadomtsev-Petviashvili equation, 29 the extended (3 + 1)-dimensional Jimbo-Miwa equation, 30 (2 + 1)-dimensional Ito equation, 31 (3 + 1)-dimensional potential-YTSF equation, 32 and (4 + 1)-dimensional KdV-like equation.…”

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

“…Solitons, lumps, breathers and rogues waves, well known to us, are all the localized waves [1][2][3][4][5][6][7][8][9]. Lump solution is a rational solution localized in all directions in space, which can be seen limit of the infinite period of the breather wave [10][11][12][13][14]. The long wave limit method is one of the effective methods to construct the multiple lump solutions and the hybrid solutions of the integrable systems that can be transformed into bilinear equations [15][16][17].…”