A Basis of Conservation Laws for Partial Differential Equations

DOI

10.2991/jnmp.2002.9.s2.6How to use a DOI?

Abstract

The classical generation theorem of conservation laws from known ones for a system of differential equations which uses the action of a canonical Lie­Bäcklund generator is extended to include any Lie­Bäcklund generator. Also, it is shown that the Lie algebra of Lie­Bäcklund symmetries of a conserved vector of a system is a subalgebra of the Lie­Bäcklund symmetries of the system. Moreover, we investigate a basis of conservation laws for a system and show that a generated conservation law via the action of a symmetry operator which satisfies a commutation rule is nontrivial if the system is derivable from a variational principle. We obtain the conservation laws of a class of nonlinear diffusion-convection and wave equations in (1 + 1)-dimensions. In fact we find a basis of conservation laws for the diffusion equations in the special case when it admits proper Lie­Bäcklund symmetries. Other examples are presented to illustrate the theory.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - A.H. Kara
AU  - F.M. Mahomed
PY  - 2002
DA  - 2002/09/02
TI  - A Basis of Conservation Laws for Partial Differential Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 60
EP  - 72
VL  - 9
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.s2.6
DO  - 10.2991/jnmp.2002.9.s2.6
ID  - Kara2002
ER  -