二维Burgers系统的增强对称性分析
Enhanced symmetry analysis of two-dimensional Burgers system
摘要：
对二维Burgers系统进行了增强对称性分析。该系统的完整的点对称群，发现使用增强版本的代数方法。用最优化的方法对Burgers系统的Lie约化进行了全面的研究，构造了新的Lie不变解。我们证明了该系统不存在局部守恒律，然后研究了隐藏的守恒律，包括潜在的守恒律。各种隐藏的对称性（连续的，离散的和潜在的）被认为是该系统以及。我们详尽地描述了解决方案的Burgers系统，它的共同解决方案，其无粘对应和二维纳维-斯托克斯方程的子集。利用微分约束的方法，这是特别有效的Burgers系统，我们构造了一些广泛的家庭的解决方案，这个系统表示的（1+1）维线性热方程的解决方案，虽然他们不相关的著名的线性化解决方案的Burgers系统的子集。
英文摘要：
We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The complete point symmetry group of this system is found using an enhanced version of the algebraic method. Lie reductions of the Burgers system are comprehensively studied in the optimal way and new Lie invariant solutions are constructed. We prove that this system admits no local conservation laws and then study hidden conservation laws, including potential ones. Various kinds of hidden symmetries (continuous, discrete and potential ones) are considered for this system as well. We exhaustively describe the solution subsets of the Burgers system that are its common solutions with its inviscid counterpart and with the two-dimensional Navier-Stokes equations. Using the method of differential constraints, which is particularly efficient for the Burgers system, we construct a number of wide families of solutions of this system that are expressed in terms of solutions of the (1+1)-dimensional linear heat equation although they are not related to the well-known linearizable solution subset of the Burgers system.
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