A Basis of Conservation Laws for Partial Differential Equations
Abdul H. Kara,Fazal M. Mahomed +1 more
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The classical generation theorem of conservation laws from known ones for a system of differential equations which uses the action of a canonical Lie-Backlund generator is extended to include any L....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–Backlund generator is extended to include any L...read more
Citations
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Noether-Type Symmetries and Conservation Laws Via Partial Lagrangians
Abdul H. Kara,Fazal M. Mahomed +1 more
TL;DR: In this article, the authors show how to construct conservation laws of Euler-Lagrange-type equations via Noether-type symmetry operators associated with what they term partial Lagrangians.
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Symmetry group classification of ordinary differential equations: Survey of some results
TL;DR: In this paper, the salient features of point symmetry group classification of scalar ODEs are presented, including linear nth-order, second-order equations and related results.
Journal ArticleDOI
Hierarchy of conservation laws of diffusion-convection equations
TL;DR: In this article, the equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations was introduced and the notion of local dependence of potentials was defined.
Journal ArticleDOI
On double reductions from symmetries and conservation laws
TL;DR: In this article, the theory of double reductions of PDEs with two independent variables that admit a Lie point symmetry and a conserved vector invariant under the symmetry is presented.
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Generalization of the double reduction theory
TL;DR: In this article, a generalization of the double reduction theory to partial differential equations of higher dimensions has been proposed and applied to the nonlinear (2+1) wave equation for arbitrary function f ( u ) and g ( u ).
References
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Book
Applications of Lie Groups to Differential Equations
TL;DR: In this paper, the Cauchy-Kovalevskaya Theorem has been used to define a set of invariant solutions for differential functions in a Lie Group.
Book
Transformation Groups Applied to Mathematical Physics
TL;DR: In this paper, the authors define the notion of invariant majorants and define an invariant transformation of a polytropic gas with respect to a group of motions, and show how to compute invariant transformations in the presence of invariants.
Book
Differential Equations: Their Solution Using Symmetries
TL;DR: In this article, the authors define Lie point transformations and symmetries of an ordinary differential equation, and how to find the Lie point transformation and symmetry of a differential equation with one symmetry and more than one symmetry.