Group classification of the generalized Emden–Fowler-type equation

Khalique, Chaudry Masood; Mahomed, F. M.; Ntsime, Basetsana P.

doi:10.1016/j.nonrwa.2008.09.020

Cited by 14 publications

(7 citation statements)

References 36 publications

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“…Following [11,15,16,19,20] (see also, e.g., [10,[21][22][23]), we look for the infinitesimal generator of the equivalence transformations of the system (1) of the form:…”

Section: Elements On Equivalence Transformationsmentioning

confidence: 99%

An Application of Equivalence Transformations to Reaction Diffusion Equations

Torrisi

Tracinà

2015

Symmetry

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In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.

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“…Following [11,15,16,19,20] (see also, e.g., [10,[21][22][23]), we look for the infinitesimal generator of the equivalence transformations of the system (1) of the form:…”

Section: Elements On Equivalence Transformationsmentioning

confidence: 99%

An Application of Equivalence Transformations to Reaction Diffusion Equations

Torrisi

Tracinà

2015

Symmetry

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“…Following [6,[11][12][13][14] (see also, e.g., [5,[15][16][17] ) we consider the infinitesimal generator of the equivalence transformations (8) of the systems (1) that reads as follows:…”

Section: Elements On Equivalence Transformationsmentioning

confidence: 99%

Weak Equivalence Transformations for a Class of Models in Biomathematics

Freire

Torrisi

2014

Abstract and Applied Analysis

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“…where x 0 is a constant. The quadrature (18) can be evaluated in terms of elliptic integrals. We can summarise our result as follows: the first integral (10), with g = K 0 F −3 , f = F xxx and F given by (18) via (16), represents a particular class of solutions of (5).…”

Section: Integrability Conditionsmentioning

confidence: 99%

“…In this case it is possible to invert the integral (18) and then write u = u(x). The first integral (10) has the form…”

Section: Case I: One Order-four Linear Factormentioning

confidence: 99%

First integrals for charged perfect fluid distributions

Kweyama¹,

Maharaj²,

Govinder³

2012

Nonlinear Analysis: Real World Applications

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We study the evolution of shear-free spherically symmetric charged fluids in general relativity. We find a new parametric class of solutions to the Einstein-Maxwell system of field equations. Our charged results are a generalisation of earlier treatments for neutral relativistic fluids. We regain the first integrals found previously for uncharged matter as a special case. In addition an explicit first integral is found which is necessarily charged.

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Group classification of the generalized Emden–Fowler-type equation

Cited by 14 publications

References 36 publications

An Application of Equivalence Transformations to Reaction Diffusion Equations

An Application of Equivalence Transformations to Reaction Diffusion Equations

Weak Equivalence Transformations for a Class of Models in Biomathematics

First integrals for charged perfect fluid distributions

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