Lie Symmetries of Differential Equations by Computer Algebra
نویسندگان
چکیده
منابع مشابه
Reduction of Differential Equations by Lie Algebra of Symmetries
The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...
متن کاملLie Symmetries of Differential Equations by Computer Algebra
Secondly combining group theory and singularity analysis we obtained some information about the similarity solutions of the fourth order generalized Boussinesq equation GBE4. It has been shown that this equation possess a three dimensional Lie algebra of the point symmetries and the similarity reductions due to these symmetries have been obtained.
متن کاملComputer Algebra Application for Determining Lie and Lie-Bäcklund Symmetries of Differential Equations
The application of computer algebra for determining Lie and Lie–Bäcklund (LB) symmetries of differential equations is considered. Algorithms for calculating the symmetries are developed and implemented on the basis of computer algebra systems REDUCE, AMP and FORMAC. The most effective and advanced program is written in FORMAC. It finds LB symmetries completely automatically. In many cases the p...
متن کاملLie Symmetries of Differential Equations Byco~uteralgebra
In this paper we restrict ourselves to Lie point symmetries an applications to the fourth order generalized Burgers equation GBE4. Using computer programs under the computer algebra package MATHEMATIC A we find a three dimensional solvable Lie algebra of point symmetries of the GBE4 equation. The similarity reductions due to these symmetries have also been obtained. The idea of applying Lie gro...
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This memoir is divided in three parts 1. Part I endeavours a general, new theory (inspired by modern CR geometry) of Lie symmetries of completely integrable PDE systems, viewed from their associated submanifold of solutions. Part II builds general combinatorial formulas for the prolongations of vector fields to jet spaces. Part III characterizes explicitly flatness of some systems of second ord...
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ژورنال
عنوان ژورنال: Mathematical and Computational Applications
سال: 1996
ISSN: 2297-8747
DOI: 10.3390/mca1010015