Lie Point Symmetries and Commuting Flows for Equations on Lattices [PDF]
, 2001 Different symmetry formalisms for difference equations on lattices are reviewed and applied to perform symmetry reduction for both linear and nonlinear partial difference equations. Both Lie point symmetries and generalized symmetries are considered and applied to the discrete heat equation and to the integrable discrete time Toda lattice.
D. Levi, P. Winternitz
arxiv +5 more sources
Special Conformal Groups of a Riemannian Manifold and Lie Point Symmetries of the Nonlinear Poisson Equation [PDF]
arXiv, 2009 We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation laws. It is shown that the projection of the Lie point symmetries on $M$ are special subgroups of the conformal ...
Yuri Bozhkov, Igor Leite Freire
arxiv +6 more sources
Lie Point Symmetries for Reduced Ermakov Systems [PDF]
, 2004 Reduced Ermakov systems are defined as Ermakov systems restricted to the level surfaces of the Ermakov invariant. The condition for Lie point symmetries for reduced Ermakov systems is solved yielding four infinite families of systems. It is shown that SL(2,R) always is a group of point symmetries for the reduced Ermakov systems.
Fernando Haas, J. Goedert
arxiv +5 more sources
Projective collineations of decomposable spacetimes generated by the Lie point symmetries of geodesic equations [PDF]
Symmetry 2021, 13(6), 1018, 2021 We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we follow a previous proposed geometric construction approach for the symmetries of differential equations.
Andronikos Paliathanasis
arxiv +3 more sources
Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation [PDF]
Mathematics, 2021 This paper studies a non-linear viscoelastic wave equation, with non-linear damping and source terms, from the point of view of the Lie groups theory.
Almudena P. Márquez, María S. Bruzón
doaj +2 more sources
Ordinary differential equations described by their Lie symmetry algebra [PDF]
Published in J. Geom. Phys. 85 (2014), 2-15, 2014 The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector fields on $\mathbb{R}^k$ and characterize Lie remarkable equations admitted by the considered Lie algebras.
Manno, Gianni +3 more
arxiv +5 more sources
Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation [PDF]
Open Physics, 2017 For a generalized KdV-Burgers-Kuramoto equation we have studied conservation laws by using the multiplier method, and investigated its first-level and second-level potential systems. Furthermore, the Lie point symmetries of the equation and the Lie point
Bruzón Maria S. +3 more
doaj +4 more sources
A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations [PDF]
, 2001 Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of Lie symmetries analytic in the neighbourhood of an equilibrium point.
Furta S. D. +5 more
arxiv +4 more sources
Lie remarkable partial differential equations characterized by Lie algebras of point symmetries [PDF]
J. Geom. Phys. 144, 314--323 (2019), 2021 Within the framework of inverse Lie problem, we give some non-trivial examples of coupled Lie remarkable equations, \textit{i.e.}, classes of differential equations that are in correspondence with their Lie point symmetries. In particular, we determine hierarchies of second order partial differential equations uniquely characterized by affine ...
Matteo Gorgone, Francesco Oliveri
arxiv +2 more sources
The geometric origin of Lie point symmetries of the Schrödinger and the Klein Gordon equations [PDF]
Int. J. Geom. Methods Mod. Phys. 11, 1450037 (2014), 2013 We determine the Lie point symmetries of the Schr\"{o}dinger and the Klein Gordon equations in a general Riemannian space. It is shown that these symmetries are related with the homothetic and the conformal algebra of the metric of the space respectively.
Andronikos Paliathanasis +1 more
arxiv +3 more sources