On the systematic approach to the classification of differential equations by group theoretical methods

Andriopoulos, K.; Dimas, S.; Leach, P. G. L.; Tsoubelis, Dimitri

doi:10.1016/j.cam.2008.11.002

Cited by 46 publications

(46 citation statements)

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“…This is a natural consequence of papers devoted to complete symmetry groups and the notion of Lie remarkability [3,23,2].…”

Section: Resultsmentioning

confidence: 93%

“…The general principle of the complete specification of differential equations in terms of their symmetries has had two lines of evolution. In one of these lines the type of Lie symmetry is restricted to point [3,23,2] and is strongly associated with the property of Lie remarkability, i.e. the equation is completely specified by the totality of the point symmetries of the equation.…”

Section: Resultsmentioning

confidence: 99%

“…The algebra given by the Lie Brackets of the six-dimensional subalgebra is still sl(2, R)⊕ s W 3 and the details of the brackets are given in Table 8. …”

Section: The Cox-ingersoll-ross Equationmentioning

confidence: 99%

“…Our belief is that those infinite-parameter generators of symmetry are not completely useless. Apart from the well-known fact that they can help to linearize a nonlinear equation, they seem to play a very important part on the classification of Differential Equations [3]. It is needless to mention their attributes with respect to the analysis of boundary and initial value problems.…”

Section: Introductionmentioning

confidence: 99%

“…(1) is the only equation of the form u xx = F (t, x, u, u t , u x , u tx , u tt ) invariant under this specific group, i.e. this Lie group completely characterizes the heat equation [3]. Since this group consists solely of point symmetries, the heat equation may be termed Lie remarkable [23,2].…”

Section: Introductionmentioning

confidence: 99%

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Complete Specification of Some Partial Differential Equations That Arise in Financial Mathematics

Dimas

Andriopoulos

Tsoubelis

et al. 2021

JNMP

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We consider some well-known partial differential equations that arise in Financial Mathematics, namely the Black-Scholes-Merton, Longstaff, Vasicek, Cox-Ingersoll-Ross and Heath equations. Our central aim is to discover any underlying connections taking into account the Lie remarkability property of the heat equation. For a few of these equations there is a known connection with the heat equation through a coordinate transformation. We investigate further that connection with the help of modern group analysis. This is realized by obtaining the Lie point symmetries of these equations and comparing their algebras with that of the heat equation. For those with an algebra identical to that of the heat equation a systematic way is shown to obtain the coordinate transformation that links them: the Lie remarkability property is a direct consequence. For the rest this is achieved only in certain subcases.

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“…This is a natural consequence of papers devoted to complete symmetry groups and the notion of Lie remarkability [3,23,2].…”

Section: Resultsmentioning

confidence: 93%

Section: Resultsmentioning

confidence: 99%

“…The algebra given by the Lie Brackets of the six-dimensional subalgebra is still sl(2, R)⊕ s W 3 and the details of the brackets are given in Table 8. …”

Section: The Cox-ingersoll-ross Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations