Recovery of the Solitons Using a Lattice Boltzmann Model

We formulate a lattice Boltzmann model which simulates Korteweg-de Vries equation by using a method of higher moments of lattice Boltzmann equation. Using a series of lattice Boltzmann equations in different time scales and the conservation law in time scale t₀, we obtain equilibrium distribution function. The numerical examples show that the method can be used to simulate soliton.