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Lie symmetries for Lie systems: applications to systems of ODEs and PDEs [PDF]
Appl. Math. Comput. 273 (2016) 435-452, 2014 A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants. Using that a Lie system can be considered as a curve in a finite-dimensional Lie algebra of vector fields, a so ...
arxiv +1 more source
Lie symmetries and reductions via invariant solutions of general short pulse equation
Frontiers in Physics, 2023 Around 1880, Lie introduced an idea of invariance of the partial differential equation (PDE) under one-parameter Lie group of transformation to find the invariant, similarity, or auto-model solutions.
Muhammad Mobeen Munir +2 more
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On Lie Symmetries of Hyperbolic Model Metric of SL(n, R) Geometry
پژوهشهای ریاضی, 2020 Introduction Symmetries of an equation are closely related to conservation laws. Noether's theorem provides a method for finding conservation laws of differential equations arising from a known Lagrangian and having a known Lie symmetry.
Rohollah Bakhshandeh Chamazkoti
doaj
Advances in Difference Equations, 2019 We investigate the point symmetries, Lie–Bäcklund symmetries for a type of dispersive water waves. We obtain some Lie transformation groups, various group-invariant solutions, and some similarity solutions.
Yufeng Zhang, Na Bai, Hongyang Guan
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Lie symmetries for two-dimensional charged particle motion
, 2002 We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation.
Abraham-Schrauner B +16 more
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Lie-Point Symmetries Preserved by Derivative
Geometry Integrability and Quantization, 2020 Conditions to guarantee that a point symmetry X of an nth-order differential equation q(n) − ω = 0 is simultaneously a point symmetry of its derived equation q(n+1) − ω = 0 are analyzed, and the possible types of vector fields established. It is further shown that only the simple Lie algebra sl(2, R) for a very specific type of realization in the plane
openaire +3 more sources
Symmetries of nonlinear ordinary differential equations: the modified Emden equation as a case study
, 2015 Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries, contact symmetries,
Chandrasekar, V. K. +2 more
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Journal of Function Spaces, 2021 In this paper, the problem of constructing the Lie point symmetries group of the nonlinear partial differential equation appeared in mathematical physics known as the generalized KdV-Like equation is discussed.
Maria Ihsane El Bahi, Khalid Hilal
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A Group Theory Approach towards Some Rational Difference Equations
Journal of Mathematics, 2019 A full Lie point symmetry analysis of rational difference equations is performed. Nontrivial symmetries are derived, and exact solutions using these symmetries are obtained.
Mensah Folly-Gbetoula +2 more
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Conservation laws, symmetry reductions, and exact solutions of some Keller–Segel models
Advances in Difference Equations, 2018 In this paper, three Keller–Segel models are considered from the point of Lie symmetry analysis, conservation laws, symmetry reduction, and exact solutions. By means of Lie symmetry analysis, we first obtain all the symmetries for the three models. Based
Lihua Zhang, Fengsheng Xu
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