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 (SCI-Expanded) identifier identifier

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.