On the isogroups of the generalised diffusion equation

Bhutani, O.P.; Vijayakumar, K.

doi:10.1016/0020-7225(90)90003-2

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Introduction2

Other Examples1

Nonclassical Symmetries1

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2015

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Cited by 18 publications

(14 citation statements)

References 7 publications

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“…14) where c is a constant, it may mentioned that the solution(3.14) is completely new that does not seen to have been reported further choosing c D 0, we obtain an exact solution reported by Vijayakumar and Bhutani[21] via scaling analysis.3.1.2. Vector field V 2 C kV4 .…”

mentioning

confidence: 56%

A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlevé analysis and Lie‐group method

El-Sayed

Moatimid

Moussa

et al. 2014

Math Methods in App Sciences

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mentioning

confidence: 56%

A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlevé analysis and Lie‐group method

El-Sayed

Moatimid

Moussa

et al. 2014

Math Methods in App Sciences

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“…Various types of diffusion equations are treated in Refs. [50,51,52]. Viscoelastic-viscoplastic rods are studied in Ref.…”

Section: Other Examplesmentioning

confidence: 99%

The Differential Form Method for Finding Symmetries

Harrison¹

2005

SIGMA

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This article reviews the use of differential forms and Lie derivatives to find symmetries of differential equations, as originally presented by Harrison and Estabrook, J. Math. Phys., 12 (1971), 653. An outline of the method is given, followed by examples and references to recent papers using the method.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

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“…In the case q = 0, without loss of generality, we may set q(x, t, u) = 1. The nonclassical method applied to (1) give rise to four determining equations for the infinitesimals.…”

Section: Nonclassical Symmetriesmentioning

confidence: 99%

“…which is the Boussinesq equation of hydrology involved in various fields of petroleum technology and ground water hydrology, several exact solutions have been obtained by using isovector method [1].…”

Section: Introductionmentioning

confidence: 99%

Similarity Reductions for a Nonlinear Diffusion Equation

Gandarias

Venero

Ramírez

1998

JNMP

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Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as local symmetries of a related auxiliary system, are obtained. For some special nonlinearities new symmetry reductions and exact solutions are derived by using the nonclassical method.

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On the isogroups of the generalised diffusion equation

Cited by 18 publications

References 7 publications

A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlevé analysis and Lie‐group method

A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlevé analysis and Lie‐group method

The Differential Form Method for Finding Symmetries

Similarity Reductions for a Nonlinear Diffusion Equation

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