Symmetries and infinitesimal symmetries of singular differential equations
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 کاملSymmetries of Differential Equations
In this chapter we discuss the foundations and some applications of Lie’s theory of symmetry groups of differential equations. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of some particular differential equations of interest. The reader interested in pursuing these matters in greater depth should consult the texts...
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Bäcklund’s Theorem, which characterizes contact transformations, is generalized to give an analogous characterization of “internal symmetries” of systems of differential equations. For a wide class of systems of differential equations, every internal symmetry comes from a first order generalized symmetry and, conversely, every first order generalized symmetry satisfying certain explicit contact...
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An infinite-dimensional algebra of all infinitesimal transformations of solutions to the self-dual Yang-Mills equations is described. As subalgebras it contains the infinitedimensional algebras of hidden symmetries related to gauge and conformal transformations.
متن کاملSymmetries, Differential Equations, and Applications: Galois Bicentenary
This special issue commemorated the bicentenary of the birth of Évariste Galois who introduced the notion of a group and made fundamental contributions to the solution of polynomial equations.The formal mathematical concept of symmetry thus came fromGalois theory. Symmetry was inaugurated andutilized in the solution of differential equations by Sophus Lie in the 1870s. The algebraic approach ha...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2002
ISSN: 0305-4470
DOI: 10.1088/0305-4470/35/24/306