A Basis of Conservation Laws for Partial Differential Equations
By Abdul Hamid Kara, Fazal Mahmood Mahomed. 2002
148 citations recorded by the source corpus.
Abstract The classical generation theorem of conservation laws from known ones for a system of differential equations which uses the action of a canonical Lie–Bäcklund generator is extended to include any Lie–Bäcklund generator. Also, it is shown that the Lie algebra of Lie–Bäcklund symmetries of a conserved vector of a system is a subalgebra of the Lie–Bäcklund 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 Lie–Bäcklund symmetries. Other examples are presented to illustrate the theory.
Subfields: Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8b15e9eda10001d9d566806a34e31697f03fcc1a
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In Numerical Analysis
In Statistical and Nonlinear Physics
Citations in the corpus
- Noether-Type Symmetries and Conservation Laws Via Partial Lagrangians (2006, methodology): “The analysis of (37) results in the cases which were obtained in [ 16 ].”
- Symmetry group classification of ordinary differential equations: Survey of some results (2007, background): “It is known that a symmetry algebra of a first integral is a subalgebra of the underlying equation that gave rise to the first integral [38].”
- Double reduction of a nonlinear (2+1) wave equation via conservation laws (2011, background): “2 [8,10].”
- Generalization of the double reduction theory (2009, background): “r provide either (1) Conservation law associated with that symmetry or (2) Conservation law that may be trivial, known already or new. A pioneering work in this direction was published by Kara et. al [5, 6]. Sjo¨berg later showed that [1, 2] when the generated conservedvector is null, i.e. the symme”