GREEN'S THEOREM AND INVARIANT TRANSFORMATIONS,

Abstract

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. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1967
Accession Number
AD0655964

Entities

People

  • Joshua N. Goldberg

Organizations

  • Syracuse University

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Equations
  • Generators
  • Linearity
  • Mathematics
  • Partial Differential Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis