Symmetries of the Eikonal equation

Ryad Ghanam, Gerard Thompson

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)137-144
Number of pages8
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume60
DOIs
Publication statusPublished - 1 Jul 2018

Fingerprint

Eikonal Equation
Symmetry
Standard Basis
Lie Symmetry
Matrix Representation
Algebra
Vector Field
Isomorphic
Standards

Keywords

  • Eikonal equation
  • Invariant solutions
  • Lie algebra
  • Symmetries

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

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

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 60, 01.07.2018, p. 137-144.

Research output: Contribution to journalArticle

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