A unified lattice Boltzmann model for some nonlinear partial differential equations

In this paper, a unified and novel lattice Boltzmann model is proposed for solving nonlinear partial differential equation that has the form DUt + αUUx + βUnUx − γUxx + δ Uxxx = F(x,t). Numerical results agree well with the analytical solutions and results derived by existing literature, which indicates the present model is satisfactory and efficient on solving nonlinear partial differential equations.