A Basis of Conservation Laws for Partial Differential Equations

• DOI: 10.2991/jnmp.2002.9.s2.6
• Publication Date: 2007-01-20T23:21:52Z
• Authors: A.H. Kara; F.M. Mahomed
• Keywords: Conservation law; Basis (linear algebra)

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