Symmetry-invariant conservation laws of partial differential equations

被引：34
|
作者：
Anco, Stephen C. [1 ]
Kara, Abdul H. [2 ]
机构：
[1] Brock Univ, Dept Math & Stat, St Catharines, ON L2S 3A1, Canada
[2] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, South Africa
来源：
EUROPEAN JOURNAL OF APPLIED MATHEMATICS | 2018年 / 29卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
conservation law; symmetry; symmetry-invariant; homogeneous; multipliers; DIRECT CONSTRUCTION METHOD; NOETHER;
D O I：
10.1017/S0956792517000055
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and symmetry-homogeneous conservation laws. The main results are applied to several examples of physically interest, including the generalized Korteveg-de Vries equation, a non-Newtonian generalization of Burger's equation, the b-family of peakon equations, and the Navier-Stokes equations for compressible, viscous fluids in two dimensions.
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页码：78 / 117
页数：40
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