Abstract: With Taylor expansion and Chapman-Enskog multi-scale expansion techniques,the equilibrium distribution functions and the correction functions are derived,and the two functions are introduced into the D1Q3 lattice Boltzmann model with two distribution functions.With this model,the initial-boundary value problem for a class of nonlinear coupled long-short wave equations is solved.For the plane wave and solitary wave solutions,the numerical simulation results verify the validity of the model for solving the nonlinear coupled initial-boundary value problems of the long-short wave equation.

Key words: long and short wave equations, lattice Boltzmann model, Taylor expansion, Chapman-Enskog multi-scale expansion