The computer calculation of Lie point symmetries of large systems of differential equations

Abstract A MACSYMA program is presented that greatly helps in the calculation of Lie symmetry groups of large systems of differential equations. The program calculates the determining equations for systems of m differential equations of order k, with p independent and q dependent variables, where m, k, p and q are arbitrary positive integers. The program automatically produces a list of determining equations for the coefficients of the vector field. This list has be... Title of program: SYMMGRP.MAX Catalogue Id: ACBI_v1_0 Nature of problem The symmetry group of a given system of differential equations modelling a physical phenomenon may be used to achieve several goals. These include the classification of the solutions of the system, the generation of new solutions from known ones, the simplification of the system by the method of symmetry reduction, to name a few. In the case where particular symmetries must be present, the symmetry group can be used to determine the validity of the modelling differential equations. Versions of this program held in the CPC repository in Mendeley Data ACBI_v1_0; SYMMGRP.MAX; 10.1016/0010-4655(91)90080-5 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要：本文介绍一款MACSYMA程序，可极大辅助大型微分方程组的李对称群（Lie symmetry group）计算工作。该程序可针对包含p个独立变量、q个因变量的k阶m个微分方程组，计算其确定方程，其中m、k、p、q均为任意正整数。程序可自动生成关于向量场系数的确定方程列表。该列表已……
程序名称：SYMMGRP.MAX
目录编号：ACBI_v1_0
问题本质：用于模拟物理现象的给定微分方程组，其对称群可用于实现多项任务，例如对系统解进行分类、从已知解生成新解、通过对称约化方法简化系统等。若需特定对称性存在时，还可借助该对称群验证建模所用微分方程的合理性。
Mendeley数据中的CPC程序库所存储的该程序版本：ACBI_v1_0；SYMMGRP.MAX；10.1016/0010-4655(91)90080-5。本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2018年）。