一类时空分数阶非线性偏微分方程的对称分析、对称约化、精确解和守恒律  

Lie symmetry analysis, symmetry reductions, explicit solutions and conservation law of a class of space-time fractional nonlinear partial differential equation

作　　者：谷琼雅 时振华 王丽真 何静 Gu Qiongya;Shi Zhenhua;Wang Lizhen;He Jing(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》2022年第2期200-213,共14页Pure and Applied Mathematics

基　　金：国家自然科学基金(11771352,11871396);陕西省自然科学基金(2020JM-431)。

摘　　要：借助对称分析方法研究了一类时空分数阶非线性偏微分方程及其特殊情形,建立了方程所允许的李代数,构造了相应的一维优化系统.进一步地,利用优化系统对所研究的方程进行了对称约化,得到了方程的群不变解.另外,利用新的守恒定律和推广的Noether算子,建立了时空分数阶微分方程的非局部守恒律.In this paper, we investigates a class of space-time fractional nonlinear partial differential equation and its special form. we obtain the Lie algebra of the equations by means of Lie symmetry analysis and construct the corresponding one-dimensional optimization system. Further, we utilize the optimal system to symmetry reduction the equation under consideration and obtain the group-invariant solution of the equation. Moreover, using the new conservation law and the generalization of the Noether operator, we establish the non-local conservation law of the space-time fractional differential equation.

关 键 词：李对称分析 优化系统 对称约化 不变解 守恒律 

分 类 号：O175.2[理学—数学]