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The lattice Boltzmann method (LBM) for the variable-coefficient forcedBurgers equation (vc-FBE) is studied by choosing the equilibrium distributionand compensatory functions properly. In our model, the vc-FBE is correctlyrecovered via the Chapman-Enskog analysis. We numerically investigate thedynamic characteristics of solitons caused by the dispersive and external-forceterms. Four numerical examples are given, which align well with the theoreticalsolutions. Our research proves that LBM is a satisfactory and efficient methodfor nonlinear evolution equations with variable coefficients.

Numerical simulation for the motions of nonautonomous solitary waves of  a variable-coefficient forced Burgers equation via the lattice Boltzmann  method