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Lie point symmetries of differential–difference equations [PDF]
Journal of Physics A: Mathematical and Theoretical, 2010 17 pages, 1 ...
LEVI, Decio, Winternitz P, Yamilov RI
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On Lie Point Symmetries in Differential Games [PDF]
SSRN Electronic Journal, 2010 A technique to determine closed-loop Nash equilibria of n-player differential games is developed when their dynamic state-control system is composed of decoupled ODEs. In particular, the theory of Lie point symmetries is exploited to achieve first integrals of such systems.
Palestini, Arsen
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Random Lie-point symmetries [PDF]
Journal of Nonlinear Mathematical Physics, 2021 We introduce the notion of a random symmetry. It consists of taking the action given by a deterministic flow that maintains the solutions of a given differential equation invariant and replacing it with a stochastic flow. This generates a random action, which we call a random symmetry.
Luis Roberto Lucinger +1 more
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Lie point symmetries and commuting flows for equations on lattices [PDF]
Journal of Physics A: Mathematical and General, 2002 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.
LEVI, Decio, Winternitz P.
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Nonlinear potential filtration equation and global actions of Lie symmetries [PDF]
Electronic Journal of Differential Equations, 2009 The Lie point symmetries of the nonlinear potential filtration equation break into five cases. Contact symmetries provide another two cases. By restricting to a natural class of functions, we show that these symmetries exponentiate to a global action ...
Mark R. Sepanski
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Lie-point symmetries of the discrete Liouville equation [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize the equation keeping the entire symmetry algebra as point symmetries.
D. Levi, MARTINA, Luigi, P. Winternitz
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FUNCTIONAL REALIZATIONS OF LIE ALGEBRAS AS NOETHER POINT SYMMETRIES OF SYSTEMS [PDF]
Acta Polytechnica, 2017 Functional realizations of Lie algebras are applied to the problem of determining Lie and Noether point symmetries of Lagrangian systems in N dimensions, particularly in the plane.
Rutwig Campoamor-Stursberg
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Note on Lie Point Symmetries of Burgers Equations
Trends in Computational and Applied Mathematics, 2010 . In this note we study the Lie point symmetries of a class of evolution equations and obtain a group classification of these equations. We also identify the classical Lie algebras that the symmetry Lie algebras are isomorphic to.
I. L. Freire
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Lie and Noether point symmetries for a class of nonautonomous dynamical systems [PDF]
Journal of Mathematical Physics, 2017 We prove two general theorems that determine the Lie and the Noether point symmetries for the equations of motion of a dynamical system that moves in a general Riemannian space under the action of a time dependent potential W(t,x)=ω(t)V(x). We apply the theorems to the case of a time dependent central potential and the harmonic oscillator and determine
Leonidas Karpathopoulos +2 more
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Lie point symmetries and ODEs passing the Painlevé test [PDF]
Journal of Nonlinear Mathematical Physics, 2021 The Lie point symmetries of ordinary differential equations (ODEs) that are candidates for having the Painlevé property are explored for ODEs of order $n =2, \dots ,5$. Among the 6 ODEs identifying the Painlevé transcendents only $P_{III}$, $P_V$ and $P_{VI}$ have nontrivial symmetry algebras and that only for very special values of the parameters.
Levi, D, Sekera, D, Winternitz, P
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