LIE, a PC program for Lie analysis of differential equations

Head, A. K.

doi:10.1016/0010-4655(93)90007-y

Cited by 161 publications

(102 citation statements)

References 3 publications

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“…The reason for this is that the powerful infinitesimal symmetry criterion is only applicable for transformations depending on continuous group parameters [6,9,13]. This is also the reason why to date no existing computer algebra package, such as [7,19,22] can be used for this purpose, because all such packages rely on the integration of the infinitesimal determining equations, which by definition only exist for Lie symmetries and are linear. Finding discrete point symmetries or the complete point symmetry group of a system of differential equations therefore has in fact to be done by hand using computer programs only for related routine calculations in interactive mode.…”

Section: The Modelmentioning

confidence: 99%

Complete point symmetry group of the barotropic vorticity equation on a rotating sphere

Cardoso-Bihlo

Popovych

2013

J Eng Math

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The complete point symmetry group of the barotropic vorticity equation on the sphere is determined. The method we use relies on the invariance of megaideals of the maximal Lie invariance algebra of a system of differential equations under automorphisms generated by the associated point symmetry group. A convenient set of megaideals is found for the maximal Lie invariance algebra of the spherical vorticity equation. We prove that there are only two independent (up to composition with continuous point symmetry transformations) discrete symmetries for this equation.

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Section: The Modelmentioning

confidence: 99%

Complete point symmetry group of the barotropic vorticity equation on a rotating sphere

Cardoso-Bihlo

Popovych

2013

J Eng Math

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“…We choose to write this as u t = f (x, t, u, u x , u xx ) since we wish to express the equation as an evolution equation with u t as the subject 6 .…”

Section: Quasi-implicit Complete Symmetry Groupsmentioning

confidence: 99%

Nonlocal Symmetries and the Complete Symmetry Group of 1 + 1 Evolution Equations

Myeni

2006

JNMP

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The complete symmetry group of a 1 + 1 linear evolution equation has been demonstrated to be represented by the six-dimensional Lie algebra of point symmetries sl(2, R)⊕ s W , where W is the three-dimensional Heisenberg-Weyl algebra. The infinite number of solution symmetries does not play a role in the complete specification of the equation. In the absence of a sufficient number of point symmetries which are not solution symmetries one must look to generalized or nonlocal symmetries to remove the deficit. This is true whether the evolution equation be linear or not. We report two Ansätze which provide a route to the determination of the required nonlocal symmetry necessary to supplement the point symmetries for the complete specification of two nonlinear 1+1 evolution equations which arise in the area of Financial Mathematics. The first of these, when reduced to its essential form, is the well-known Burgers' equation.

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“…We use Program LIE's [14,29] capacity to indicate divisors by factors of combinations of the parameters in the symmetry analysis of (3.2), videlicet…”

Section: Symmetry Analysis Of the Related Second-order Equationmentioning

confidence: 99%

Properties of the Dominant Behaviour of Quadratic Systems

Maharaj

2006

JNMP

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We study the dominant terms of systems of Lotka-Volterra-type which arise in the the mathematical modelling of the evolution of many divers natural systems from the viewpoint of both symmetry and singularity analyses. The connections between an increase in the amount of symmetry possessed by the system and the possession of the Painlevé Property are noted. For specific values of the parameters of the system we see that possession of the Painlevé Property is characterised by a Left Painlevé Series rather than the more standard Right Painlevé Series.

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LIE, a PC program for Lie analysis of differential equations

Cited by 161 publications

References 3 publications

Complete point symmetry group of the barotropic vorticity equation on a rotating sphere

Complete point symmetry group of the barotropic vorticity equation on a rotating sphere

Nonlocal Symmetries and the Complete Symmetry Group of 1 + 1 Evolution Equations

Properties of the Dominant Behaviour of Quadratic Systems

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