AI 中文总结
本文针对（1+2）维Kudryashov-Sinelshchikov方程，通过李对称分析、Painlevé分析与乘子法，得到其无限维李代数、Laurent级数解及四类守恒律，验证了方程的守恒性质。
AI 中文摘要
含气泡液体中的压力波传播是流体动力学与数学物理领域的重要研究问题。Kudryashov-Sinelshchikov方程是研究含气泡液体中非线性波动的有用数学框架，可描述液体与气相之间的黏性、热交换效应。本文研究降维后的（1+2）维Kudryashov-Sinelshchikov方程，这是一个四阶非线性偏微分方程。通过分析李对称，因存在任意函数，得到了无限维李代数；利用这些向量场之间的交换关系，并选取任意函数的特定形式，可将该控制偏微分方程约化为四阶常微分方程。随后对约化方程进行Painlevé分析，得到Laurent级数形式的解；此外，采用乘子法获取守恒向量，并分析该方程的守恒性质，共得到四种情形，且所有情形下的守恒律均通过验证。
英文摘要
The wave propagation of pressures in liquids that contain gas bubbles are an important concern in fluid dynamics and mathematical physics. The Kudryashov Sinelshchikov equation offers a useful mathematical framework in the study of nonlinear wave motion in bubbly liquids with reference to the effects of viscosity and heat exchange between liquid and gaseous phases. This paper examines the dimensional reduced (1 + 2)-dimensional Kudryashov Sinelshchikov equation, a fourth-order nonlinear partial differential equation. Analyzing the Lie symmetry, an infinite dimension Lie algebra is obtained because of the presence of arbitrary functions. By applying the commutative relation between these vector fields and choosing the specific forms for the arbitrary functions, helps the governing PDE to reduce to fourth order ODEs. The reduced equations are then investigated using the Painleve analysis to give solutions in the form of Laurent series. In addition, multiplier approach is used to obtain the conserved vectors and to analyzed conservations properties of the equation. We obtain four cases and the Conservation laws were verified for all the cases.
