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Lie Point Symmetries and Dynamical Systems
1993The notion and the peculiar properties of Lie point symmetries in the context of first-order time evolution ODE are examined, also in comparison with different situations (e.g. PDE, Hamiltonian problems). We obtain in particular that Lie symmetries provide an extension to the nonlinear case of a useful “reduction lemma”, and some applications ...
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Lie point-symmetries and Poincare normal forms for dynamical systems
Journal of Physics A: Mathematical and General, 1990The problem of finding the extended Lie-point time-independent symmetries of autonomous systems of ordinary differential equations is compared with the Poincare procedure of reducing the system to linear or normal form, showing a close relationship between the two problems.
CICOGNA, GIAMPAOLO, Gaeta G.
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Lie Point Symmetries and Exact Solutions of Couple KdV Equations
Communications in Theoretical Physics, 2007Summary: The simple Lie point symmetry reduction procedure is used to obtain infinitely many symmetries to a new integrable system of coupled KdV equations. Using some symmetry subalgebra of the equations, five types of the significant similarity reductions are obtained by virtue of the Lie group approach, and obtain abundant solutions of the coupled ...
Qian, Su-Ping, Tian, Li-Xin
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Lie point symmetries of Stratonovich stochastic differential equations
Journal of Physics A: Mathematical and Theoretical, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Lie symmetries of nonlinear systems with unknown inputs
Mechanical Systems and Signal Processing, 2023Xiaodong Shi, Manolis N Chatzis
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Lie point symmetries of a general class of PDEs: The heat equation
Journal of Geometry and Physics, 2012Andronikos Paliathanasis +1 more
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