A lattice Boltzmann model for the ion- and electron-acoustic solitary waves in beam-plasma system

In this paper, a lattice Boltzmann model for the ion- and electron-acoustic solitary waves in beam-plasma system is proposed. By using the Chapman–Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. By selecting the appropriate moments of the equilibrium distribution functions, the macroscopic equations are recovered. In numerical examples, we simulate the propagation of the ion- and electron-acoustic solitary waves. Numerical results show that the lattice Boltzmann method is an effective tool for the study of the ion- and electron-acoustic solitary waves in plasma.