Symmetry and conservation law structures of some anti-self-dual (ASD) manifolds

Basingwa, J; Kara, A. H.; Bokhari, Ashfaque H.; Mousa, R A; Zaman, F. D.

doi:10.1007/s12043-016-1258-y

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…A detailed symmetry analysis of ASD-Einstein manifolds has been done in [3] .The metric on the ASD Ricci-flat is locally given by ds 2 g ab being the metric of this space, g = g ab its determinant, g ab the inverse of g ab , where ,b = ∂ b and is the D'Alembertian, sometimes called the "box" operator.…”

Section: Wave Equations On the Asd-einstein Manifoldmentioning

confidence: 99%

Some geometric structures of wave equations on manifolds of `neutral signatures'

Bashingwa¹,

Kara²

2016

Preprint

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Section: Wave Equations On the Asd-einstein Manifoldmentioning

confidence: 99%

Some geometric structures of wave equations on manifolds of `neutral signatures'

Bashingwa¹,

Kara²

2016

Preprint

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“…However, Lie symmetries are very useful and for the study of ordinary differential equations. Some studies on the symmetry analysis on the geodesic equations in curved spaces are presented in [28][29][30][31]. Finally, in [32] a discussion is given on the novelty on the application of the Lie symmetry analysis in gravitational physics and cosmology.…”

Section: Introductionmentioning

confidence: 99%

Similarity transformations and linearization for a family of dispersionless integrable PDEs

Paliathanasis

2022

Preprint

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We apply the theory of Lie point symmetries for the study of a family of partial differential equations which are integrable by the hyperbolic reductions method and are reduced to members of the Painlevé transcendents. The main results of this study is that from the application of the similarity transformations provided by the Lie point symmetries all the members of the family of the partial differential equations are reduced to second-order differential equations which are maximal symmetric and can be linearized.

show abstract

“…However, Lie symmetries are very useful for the study of ordinary differential equations. Some studies on the symmetry analysis on the geodesic equations in curved spaces are presented in [28][29][30][31]. Finally, in [32] a discussion is given on the novelty on the application of the Lie symmetry analysis in gravitational physics and cosmology.…”

Section: Introductionmentioning

confidence: 99%

Similarity Transformations and Linearization for a Family of Dispersionless Integrable PDEs

Paliathanasis

2022

Symmetry

View full text Add to dashboard Cite

We apply the theory of Lie point symmetries for the study of a family of partial differential equations which are integrable by the hyperbolic reductions method and are reduced to members of the Painlevé transcendents. The main results of this study are that from the application of the similarity transformations provided by the Lie point symmetries, all the members of the family of the partial differential equations are reduced to second-order differential equations, which are maximal symmetric and can be linearized.

show abstract

Symmetry and conservation law structures of some anti-self-dual (ASD) manifolds

Cited by 9 publications

References 21 publications

Some geometric structures of wave equations on manifolds of `neutral signatures'

Some geometric structures of wave equations on manifolds of `neutral signatures'

Similarity transformations and linearization for a family of dispersionless integrable PDEs

Similarity Transformations and Linearization for a Family of Dispersionless Integrable PDEs

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