General propagation lattice Boltzmann model for a variable-coefficient compound KdV-Burgers equation

A Unified Lattice Boltzmann Model for Fourth Order Partial Differential Equations with Variable Coefficients

“…LBM attracts more and more experts and scholars’ attention internationally. Researchers mainly use LBM to simulate fluid flow [ 7 , 8 ] and solve PDEs [ 9 , 10 , 11 , 12 , 13 , 14 ].…”

“…Lan et al. [ 12 ] investigated a general propagation LB model and successfully simulated KdV-Burgers equation with TDVCs through adjusting the propagation step. Following the idea in the work of Chai and his collaborators, Qiao et al.…”

Solitary waves and modulation instability with the influence of fractional derivative order in nonlinear left-handed transmission line

“…Nevertheless, some historical summaries of the developments of the fractional calculation developments used can be found in the works of [4,5] and [6]. Several methods to obtain exact solutions or even soliton solutions to nonlinear partial differential equations have been proposed, such as the Bäcklund transformation method [15], the Hirota's bilinear method [16], the inverse scattering transform method [17], the extended tanh method [18], the Adomian approximation [19], the variational method [20], the variational iteration method [21], the various Lindstedt-Poincare methods [22], the Adomian decomposition method (ADM) [23,24,25,26,27], the F-expansion method [28], the exp-function method [29], the homotopy perturbation method [30,31] and the results on the acquired solitary waves were successful thanks to the different mathematical methods recently used such as the Darboux transformation [32,33,34,35],Hirota-Riemann method [36],numerical simulation [37],Hirota method [38].…”

Stripe solitons and lump solutions for a generalized Kadomtsev–Petviashvili equation with variable coefficients in fluid mechanics

“…The organization of this paper is as follows: Section 2 presents the lump solutions for Eq. (1) based on Hirota's bilinear form and symbolic computation [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Section 3 discusses the interaction solutions between lump solution and the stripe soliton.…”