### Abstract

The infinitesimal algebra of Lie symmetries of the Eikonal equation is shown to be isomorphic to o(n+1,2) when there are n independent variables. An explicit basis is found that is aligned with the standard basis coming from the standard matrix representation of o(n+1,2) thereby making it possible to read off inequivalent one-dimensional symmetry vector fields. The symmetries are used to construct various solutions of the Eikonal equation.

Original language | English |
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Pages (from-to) | 137-144 |

Number of pages | 8 |

Journal | Communications in Nonlinear Science and Numerical Simulation |

Volume | 60 |

DOIs | |

Publication status | Published - 1 Jul 2018 |

### Fingerprint

### Keywords

- Eikonal equation
- Invariant solutions
- Lie algebra
- Symmetries

### ASJC Scopus subject areas

- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics

### Cite this

*Communications in Nonlinear Science and Numerical Simulation*,

*60*, 137-144. https://doi.org/10.1016/j.cnsns.2018.01.007

**Symmetries of the Eikonal equation.** / Ghanam, Ryad; Thompson, Gerard.

Research output: Contribution to journal › Article

*Communications in Nonlinear Science and Numerical Simulation*, vol. 60, pp. 137-144. https://doi.org/10.1016/j.cnsns.2018.01.007

}

TY - JOUR

T1 - Symmetries of the Eikonal equation

AU - Ghanam, Ryad

AU - Thompson, Gerard

PY - 2018/7/1

Y1 - 2018/7/1

N2 - The infinitesimal algebra of Lie symmetries of the Eikonal equation is shown to be isomorphic to o(n+1,2) when there are n independent variables. An explicit basis is found that is aligned with the standard basis coming from the standard matrix representation of o(n+1,2) thereby making it possible to read off inequivalent one-dimensional symmetry vector fields. The symmetries are used to construct various solutions of the Eikonal equation.

AB - The infinitesimal algebra of Lie symmetries of the Eikonal equation is shown to be isomorphic to o(n+1,2) when there are n independent variables. An explicit basis is found that is aligned with the standard basis coming from the standard matrix representation of o(n+1,2) thereby making it possible to read off inequivalent one-dimensional symmetry vector fields. The symmetries are used to construct various solutions of the Eikonal equation.

KW - Eikonal equation

KW - Invariant solutions

KW - Lie algebra

KW - Symmetries

UR - http://www.scopus.com/inward/record.url?scp=85043350352&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043350352&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2018.01.007

DO - 10.1016/j.cnsns.2018.01.007

M3 - Article

VL - 60

SP - 137

EP - 144

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

ER -