Lattice Boltzmann model for a generalized Gardner equation with time-dependent variable coefficients

On a generalized variable‐coefficient Gardner equation with linear damping and dissipative terms

“…Finally, Equation 1 was studied from the point of view of numerical simulations. 10 The authors showed that the numerical results obtained agree with the analytical solutions, indicating that the lattice Boltzmann model is a satisfactory and efficient algorithm. In particular, they took into account different numerical simulations, for example, the propagation and interaction of the solitons, the evolution of the non-propagating soliton, and the propagation of the double-pole solutions.…”

“…Furthermore, the authors obtained multi‐soliton solutions, breather solutions, and a Bäcklund transformation by mapping this equation into its bilinear form. Finally, Equation was studied from the point of view of numerical simulations . The authors showed that the numerical results obtained agree with the analytical solutions, indicating that the lattice Boltzmann model is a satisfactory and efficient algorithm.…”

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 ].…”

“…Lai and Ma [ 9 ] presented a lattice Boltzmann (LB) model for fourth order generalized Kuramoto-Sivashinsky (GKS) equation, in which an amending function assumed to be second order of time step is applied to recover the GKS equation correctly. Hu and their collaborators [ 10 ] developed a LB model to solve a generalized Gardner equation with time-dependent variable coefficients (TDVCs) by means of adding a compensation function to the evolution equation. In order to solve a class of PDEs with the order up to six, Chai et al.…”

Numerical Simulation of Fuzzy Wave-Like Equations with Spatial Variable Coefficients by Lattice Boltzmann Method

“…The lattice Boltzmann method (LBM) [1][2], as an effective numerical approach, has achieved success in simulating some complex fluid flows. Recently, LBM has been extended successfully to simulate some nonlinear evolution equations(NLEEs), such as , KdV-Burgers equation with variable coefficients [1], Fokker-Planck equation with [3], a class of convection-diffusion equations with variable coefficients [4], generalized Gardner equation with time dependent variable coefficients [5][6] and so on.…”