Results 21 to 30 of about 530,977 (309)
Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries [PDF]
Dans Algebraic Biology 2007 4545 (2007) 277--291, 2006 Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine derivations} that induces \emph{expanded} Lie point symmetries of considered system. By rewriting original problem in
G. Bluman +5 more
arxiv +10 more sources
Polynomial Time Nondimensionalisation of Ordinary Differential Equations via their Lie Point Symmetries [PDF]
, 2006 Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equation.
Évelyne Hubert, Alexandre Sedoglavic
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Lie Point Symmetry and Physics Informed Networks [PDF]
arXiv, 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.
Akhound-Sadegh, Tara +4 more
arxiv +3 more sources
Lie point symmetries for generalised Fisher's equations describing tumour dynamics
Mathematical Biosciences and Engineering, 2021 A huge variety of phenomena are governed by ordinary differential equations (ODEs) and partial differential equations (PDEs). However, there is no general method to solve them. Obtaining solutions for differential equations is one of the greatest problem
Salvador Chulián +3 more
doaj +5 more sources
On differential equations characterized by their Lie point symmetries [PDF]
Journal of Mathematical Analysis and Applications, 2006 AbstractWe study the geometry of differential equations determined uniquely by their point symmetries, that we call Lie remarkable. We determine necessary and sufficient conditions for a differential equation to be Lie remarkable. Furthermore, we see how, in some cases, Lie remarkability is related to the existence of invariant solutions.
Gianni Manno +2 more
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Partial Lie-point symmetries of differential equations [PDF]
Journal of Physics A: Mathematical and General, 2001 When we consider a differential equation $ =0$ whose set of solutions is ${\cal S}_ $, a Lie-point exact symmetry of this is a Lie-point invertible transformation $T$ such that $T({\cal S}_ )={\cal S}_ $, i.e. such that any solution to $ =0$ is tranformed into a (generally, different) solution to the same equation; here we define {\it partial ...
Giampaolo Cicogna, Giuseppe Gaeta
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Lie-point symmetries of the Lagrangian system on time scales [PDF]
arXiv, 2012 This letter investigates the Lie point symmetries and conserved quantities of the Lagrangian systems on time scales, which unify the Lie symmetries of the two cases for the continuous and the discrete Lagrangian systems. By defining the infinitesimal transformations' generators and using the invariance of differential equations under infinitesimal ...
Ping-Ping, Cai +3 more
arxiv +3 more sources
Lie point symmetries of the Lane?Emden systems
Journal of Mathematical Analysis and Applications, 2004 AbstractIt is shown that a Lie point symmetry of the Lane–Emden system is a Noether symmetry if and only if its parameters belong to the critical hyperbola.
Yuri Bozhkov
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Lie point and variational symmetries in minisuperspace Einstein gravity [PDF]
Journal of Physics A: Mathematical and Theoretical, 2014 Latex source file 20 pages, no ...
T. Christodoulakis +2 more
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Lie point symmetries and first integrals: The Kowalevski top [PDF]
Journal of Mathematical Physics, 2003 We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci [J. Math. Phys. 37, 1772–1775 (1996)] is essential. Noether’s theorem is neither necessary nor considered.
M. Marcelli, M. C. Nucci
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