A Geometric View on the Symmetries of 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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Internal Symmetries of Differential Equations
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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ژورنال
عنوان ژورنال: Proceedings
سال: 2018
ISSN: 2504-3900
DOI: 10.3390/proceedings2010073