扰动Burgers-Korteweg-de Vries方程描述的周期结构
Periodic structures described by the perturbed Burgers-Korteweg-de Vries equation
摘要：
研究扰动Burgers-Korteweg-de Vries方程.该方程可用于描述含气泡液体中的非线性波，也可用于描述沿斜面流下的流体层上的非线性波。我们使用Painlevé方法研究这个方程的可积性。我们证明了扰动的Burgers-Korteweg-de Vries方程不属于可积方程类。经典和非经典的对称性承认这个方程和相应的对称性约化的构造。发现了由Burgers-Korteweg-de Vries方程描述的新型周期性解析结构。
英文摘要：
We study the perturbed Burgers-Korteweg-de Vries equation. This equation can be used for the description of nonlinear waves in a liquid with gas bubbles and for the description of nonlinear waves on a fluid layer flowing down an inclined plane. We investigate the integrability of this equation using the Painlevé approach. We show that the perturbed Burgers-Korteweg-de Vries equation does not belong to the class of integrable equations. Classical and nonclassical symmetries admitted by this equation and corresponding symmetry reductions are constructed. New types of periodic analytical structures described by the Burgers-Korteweg-de Vries equation are found.
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