一类非线性抛物型方程的最优系统和对称破缺

Optimal systems and symmetry breaking for a class of nonlinear parabolic equations

研究了一类非线性抛物型方程的对称群、最优系统和对称破缺.首先给出了这个方程的七维的李对称群,利用伴随作用的不变量,建立了其李对称群的最优系统.在此基础上,构建了二维和三维最优系统,并研究了该方程的对称破缺,基于其最优系统的子代数,给出了更一般的一类抛物型方程的分类.

In this paper, symmetry groups, optimal systems and symmetry breaking of a class of nonlinear parabolic equations are studied. Firstly, the seven-dimensional Lie symmetry group of the equation is given, and the one-dimensional optimal systems of the Lie symmetry group by invariants of the adjoint representation is constructed. Based on one-dimensional optimal systems, the two-dimensional and three-dimensional optimal systems of the symmetry group are derived. Finally, symmetry breaking of the equation is also studied. In terms of the subalgebra of the optimal systems, a classification to the more general class of parabolic equations is provided.