Green's Theorem and Invariant Transformations

Conservation laws are derived with the use of Green's theorem. These are studied specifically for the wave equation. A trivial class of invariant transformations exists which maps solutions into solutions. The mapping consists in the addition of a particular solution to all solutions. Because o...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 1968-05, Vol.9 (5), p.674-679
Main Author: Goldberg, Joshua N.
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Conservation laws are derived with the use of Green's theorem. These are studied specifically for the wave equation. A trivial class of invariant transformations exists which maps solutions into solutions. The mapping consists in the addition of a particular solution to all solutions. Because of the linearity of the wave equation, this sum will again be a solution. It is shown that this class of transformations has the Newman‐Penrose constants among its generators. Calculations are carried out explicitly for the scalar wave equation and for Maxwell's equations.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1664627