非线性演化方程的切对称群分析  

Contact symmetry group analysis for a nonlinear evolution equation

作　　者：高晓润 黄晴 Gao Xiaorun;Huang Qing(School of Mathematics,Northwest University,Xi′an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2021年第3期264-270,共7页Pure and Applied Mathematics

基　　金：国家自然科学基金(11871396,11771352);陕西省自然科学基金(2018JM1005).

摘　　要：将优化系统的概念推广应用至切代数,并以一个二阶非线性演化方程为例,给出了方程所容许的切对称,建立了切对称的一维优化系统.并利用优化系统对所研究的方程进行了对称约化,得到了与不等价对称相对应的约化方程和不变解.In this paper,we generalize the concept of optimal system to make it applicable for contact algebras.To illustrate the application of this approach,we study contact symmetries of a second-order nonlinear evolution equation,and establish the one-dimensional optimal systems generated by contact symmetries.In addition,based on the one-dimensional optimal systems,the symmetry reductions for the equation under study are performed.The reduced equations and exact solutions associated with the inequivalent symmetries are obtained.

关 键 词：切对称 优化系统 对称约化 约化方程 不变解 

分 类 号：O175.2[理学—数学]