NLS-KDV方程的格子Boltzmann方法
Lattice Boltzmann Method for the NLS-KDV Equation
DOI: 10.12677/pm.2025.155172, PDF,   
作者: 董亚茹, 戴厚平, 王 晶：吉首大学数学与统计学院，湖南 吉首
关键词: NLS-KDV方程；格子Boltzmann方法；Taylor展开；NLS-KDV Equation； Lattice Boltzmann Method； Taylor Expansion
摘要: 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。
Abstract: 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.
文章引用：董亚茹, 戴厚平, 王晶. NLS-KDV方程的格子Boltzmann方法[J]. 理论数学, 2025, 15(5): 232-240. https://doi.org/10.12677/pm.2025.155172

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