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On differential equations characterized by their Lie point symmetries [PDF]
Journal of Mathematical Analysis and Applications, 2007 The authors study differential equations which are uniquely determined by their Lie point symmetries; they call such equations Lie remarkable. Using the jet bundle formalism a geometric characterisation of these equations is given. As two larger examples, minimal submanifold equations and Monge-Ampère equations are considered in some detail.
Raffaele Vitolo +2 more
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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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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
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Lie Point Symmetry and Physics-Informed Networks
Advances in Neural Information Processing Systems 36, 2023 Symmetries have been leveraged to improve the generalization of neural networks through different mechanisms from data augmentation to equivariant architectures. However, despite their potential, their integration into neural solvers for partial differential equations (PDEs) remains largely unexplored.
Tara Akhound-Sadegh +4 more
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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 point symmetries of a general class of PDEs: The heat equation
Journal of Geometry and Physics, 2012 We give two theorems which show that the Lie point and the Noether symmetries of a second-order ordinary differential equation of the form (D/(Ds))(((Dx^{i}(s))/(Ds)))=F(x^{i}(s),x^{j}(s)) are subalgebras of the special projective and the homothetic algebra of the space respectively.
Michael Tsamparlis +1 more
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Lie-point symmetries and nonlinear dynamical systems
Mathematical and Computer Modelling, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giuseppe Gaeta, G Cicogna
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Lie Symmetries of the Wave Equation on the Sphere Using Geometry
DynamicsA semilinear quadratic equation of the form Aij(x)uij=Bi(x,u)ui+F(x,u) defines a metric Aij; therefore, it is possible to relate the Lie point symmetries of the equation with the symmetries of this metric. The Lie symmetry conditions break into two sets:
Michael Tsamparlis +1 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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Advances in Nonlinear Analysis, 2023 In the present work, we find the Lie point symmetries of the Ricci flow on an n-dimensional manifold, and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics.
López Enrique +2 more
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