Lie symmetries of differential equations and dynamical systems
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...
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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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For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In connection with this a new algorithm for computing the Lie symmetries of a linear ordinary differen...
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Lie symmetry analysis of differential equations provides a powerful and fundamental framework to the exploitation of systematic procedures leading to the integration by quadrature (or at least to lowering the order) of ordinary differential equations, to the determination of invariant solutions of initial and boundary value problems, to the derivation of conservation laws, to the construction o...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1982
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700005323