Approximate symmetries and conservation laws with applications


Kara A., Mahomed F., Unal G.

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, vol.38, no.9, pp.2389-2399, 1999 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 9
  • Publication Date: 1999
  • Doi Number: 10.1023/a:1026684004127
  • Journal Name: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.2389-2399

Abstract

The relationship between the approximate Lie-Backlund symmetries and the approximate conserved forms of a perturbed equation is studied. It is shown that a hierarchy of identities exists by which the components of the approximate conserved vector or the associated approximate Lie-Backlund symmetries are determined by recursive formulas. The results are applied to certain classes of linear and nonlinear wave equations as well as a perturbed Korteweg-de Vries equation. We construct approximate conservation laws for these equations without regard to a Lagrangian.