Lattice Boltzmann Method for the NLS-KDV Equation

建立一维格子Boltzmann模型的演化方程，运用Taylor展开和Chapman-Enskog多尺度分析技术，推导出能够恢复一类非线性耦合的NLS-KDV方程的平衡态分布函数和修正函数。最后，数值算例验证出该方法的计算结果与给出的精确解有很好的一致性。The evolution equations of the one-dimensional lattice Boltzmann model are established, and the equilibrium distribution function and the correction function that can recover a class of nonlinearly coupled NLS-KDV equations are derived by using Taylor expansion and Chapman-Enskog multiscale analysis techniques. Finally, numerical examples verify that the computational results of the method are in good agreement with the given exact solutions.