The N-soliton solution and localized wave interaction solutions of the (2+1)-dimensional generalized Hirota-Satsuma-Ito

Lump-Type Wave and Interaction Solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili Equation

“…where θ 1 , θ 2 , and R are given by (19) and the arbitrary real parameters m 1 , n 1 , v 1 , and w 1 need to satisfy condition (20).…”

“…Some properties about lump-type wave solution are demonstrated in virtue of the theoretical analysis and graphical representation. In addition, many researchers have also investigated the interaction between lump-type wave and other type of solitary wave solutions, and some interesting interaction phenomena have been shown [16][17][18][19][20][21][22][23][24].…”

Rational Localized Waves and Their Absorb-Emit Interactions in the (2 + 1)-Dimensional Hirota–Satsuma–Ito Equation

“…Periodic wave solutions and their asymptotic analysis were presented in References [5,6]. The Hirota-Satsuma shallow water wave model has a higher dimensional generalized form [7][8][9][10][11][12]:…”

Soliton, breather, lump and their interaction solutions of the ($2+1$)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

“…A set of systematic methods have been used in the literature to obtain reliable treatments of nonlinear evolution equations. So far, researchers have established several methods to find the exact solutions, including the inverse scattering transform [1], the Bäcklund transformation [2][3][4][5], the Darboux transformation [6][7][8][9][10][11][12][13][14], the Riemann-Hilbert approach [15][16][17] and Hirota's bilinear method [18][19][20][21][22][23][24][25][26][27][28], Jacobian elliptic function method and modified tanh-function method [29][30][31][32][33]. Each of these approaches has its features, Hirota's bilinear method is widely popular due to its simplicity and directness.…”