A lattice Boltzmann model for the generalized Boussinesq equation

A lattice Boltzmann model is developed for the simulation of the generalized nonlinear Boussinesq equation. Through adding a differential operator of the diffusion term as a source term to the evolution equation the macroscopic equation is recovered with higher-order truncation error. Detailed numerical simulations for the motion of the soliton solutions of the Boussinesq equation are performed and the numerical results agree well with the exact solutions. The results show that the lattice Boltzmann method is an efficient algorithm with excellent long-time numerical behaviors for the motion of the soliton solutions.