Study of lump solutions to an extended Calogero-Bogoyavlenskii-Schiff equation involving three fourth-order terms

Abstract

A new generalized fourth-order nonlinear differential equation originating from the Calogero-Bogoyavlenskii-Schiff equation with an extra term is studied. In terms of the coefficients of this combined nonlinear equation, a class of lump solutions is constructed by the Hirota bilinear method and calculated through the symbolic computation system of Maple. Furthermore, the affection of the extended item on the solution is explored. Two particular lump solutions with special choices of the involved parameters are generated and plotted, as illustrative examples.

New solitary wave solutions of the Sawada-Kotera equation and its bidirectional form

“…In [20], the (2+1)-dimensional bilinear p-SawadaKotera (pSK) equation has been investigated; then two different forms of solutions, including bright lump wave and brightdark lump wave are obtained. Some other examples of nonlinear models can be found in the literature, including [21][22][23][24][25][26][27][28][29][30].…”

Comment on ‘Study of lump solutions to an extended Calogero-Bogoyavlenskii-Schiff equation involving three fourth-order terms’ (2020 Phys. Scr. 95 095207)

“…Recent activities in nonlinear optics, fluid dynamics and plasma physics have been impressive [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], while in those fields and some other fields of sciences have arisen types of the nonlinear evolution equations (NLEEs) [4][5][6][7][8][9][10][11][12][13][14][15][16][17], one of which, i.e., System (1), is presented right below. An auto-Bäcklund transformation has been seen to go as a package of the partial differential equations relating a set of the solutions for an NLEE to another set of the solutions for the same NLEE [16][17][18][19][20][21][22].…”

“…In nonlinear optics, fluid dynamics and plasma physics, Reference [4], the paper commented, has investigated certain bilinear form and lump solutions for a (2+1)-dimensional extended Calogero-Bogoyavlenskii-Schiff system, i.e.,…”

“…••• = i 1, 2, ,6) representing some constants as well [4,5]. Also of current interest, certain soliton, breather and lump solutions for System (1) have been obtained [5].…”

“…Our plan will be to make the issue raised in [4] more complete. For System (1), since no Bäcklund transformation has been reported as yet, making use of the Hirota method [23] and symbolic computation [24][25][26][27][28][29], we will construct three sets of the bilinear auto-Bäcklund transformations along with some analytic solutions, based on Bilinear Form (3).…”