Lump solutions and bilinear Bäcklund transformation for the $$(4+1)$$-dimensional Fokas equation

On Highly Dimensional Elastic and Nonelastic Interaction between Internal Waves in Straight and Varying Cross-Section Channels

“…(2) e obtained solutions: is part gives a comparison between our obtained solutions and those obtained in previously accepted papers. In [41][42][43] by Wan-Jun Zhang and Tie-Cheng Xia, Ruoxia Yao, Yali Shen, and Zhibin Li, and Wei Li and Yinping Liu, respectively, who applied the Hirota bilinear method, the bilinear form, and Hirota method, receptively to a fractional nonlinear (4 + 1)dimensional Fokas equation, many distinct types of solutions for these fractional nonlinear models were obtained. All our obtained solutions of the investigated model are new and different from those obtained in [41][42][43].…”

“…In this research, we study the nonlinear fractional (4 + 1)-dimensional Fokas model that is mathematically given by [41][42][43]…”

A new (n+1)-dimensional generalized Kadomtsev-Petviashvili equation: Integrability characteristics and localized solutions

“…where δ 2 = γ/(3β), and λ is an arbitrary constant parameter. The two equations in (21) are compatible provided that q satisfies Eq. ( 8), i.e., ϕ x1x1t = ϕ tx1x1 .…”

“…As is well known, many researches focus on the integrable systems in (1+1)-dimensions and (2+1)-dimensions [6][7][8][9][10][11][12][13][14][15][16]. Considering the fact that the real situation is in (3+1)-dimensions, a number of (3+1)-dimensional equations have been proposed starting from the lower dimensional integrable models, and their various types of exact solutions have been presented [17][18][19][20][21][22]. Among these (3+1)-dimensional equations, most of them do not pass the conventional integrability test.…”

Bilinear Bäcklund transformations, lump solutions and interaction solutions for (4+1)-dimensional variable-coefficient Fokas equation

“…Because of the significance and wide applications of higher-dimensional equations in the field of mathematical physics, lots of researchers have paid attention to equation (2). Solitons ( [5], [6]), quasi-periodic solutions ( [7]), lumps ( [8], [9]), and lump-soliton solutions ( [10], [11]), bilinear Bäcklund transformation( [12]), high-order rational and semi-rational solutions( [13]), traveling wave solutions( [14]), Lie symmetry analysis and exact invariant solutions( [15]) for the 4D Fokas equation have been investigated. Although there are many studies for 4D Fokas equation ( 2), but few results on variable-coefficient equation (1).…”