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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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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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On differential equations characterized by their Lie point symmetries
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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Lie remarkable partial differential equations characterized by Lie algebras of point symmetries [PDF]
Journal of Geometry and Physics, 2019 22 ...
Matteo Gorgone, Francesco Oliveri
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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 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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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 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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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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Lie group analysis for short pulse equation [PDF]
AUT Journal of Mathematics and Computing, 2020 In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given.
Mehdi Nadjafikhah
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