六阶广义Boussinesq方程(带有高阶空间色散)的对称分析与守恒律
Symmetry Analysis and Conservation Laws for a Generalized Sixth-Order Boussinesq Equation (with High-Order Spatial Dispersion)
摘要: 本文对六阶广义Boussinesq方程(带有高阶空间色散)进行了对称分析与守恒律的研究。首先，通过Lie对称分析方法，给出了六阶Boussinesq方程的Lie对称分类定理。其次，基于Lie对称对六阶Boussinesq方程进行了对称约化。最后，基于新守恒定理，构造了六阶Boussinesq方程的守恒律。由此，为进一步研究六阶Boussinesq方程的精确解或近似解打好了基础。
Abstract: This paper investigates the symmetry analysis and conservation laws for a generalized sixth-order Boussinesq equation with high-order spatial dispersion. Firstly, using the Lie symmetry analysis method, the Lie symmetry classification theorem for the sixth-order Boussinesq equation is presented. Secondly, symmetry reductions are performed based on the obtained Lie symmetries. Finally, by applying the new conservation theorem, conservation laws for the sixth-order Boussinesq equation are constructed. Thereby, this work lays a foundation for further research on exact or approximate solutions of the sixth-order Boussinesq equation.
文章引用：张子祎, 银山. 六阶广义Boussinesq方程(带有高阶空间色散)的对称分析与守恒律[J]. 理论数学, 2026, 16(2): 144-153. https://doi.org/10.12677/pm.2026.162043

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