A new conservation theorem
By Nail H. Ibragimov. 2007
896 citations recorded by the source corpus.
A general theorem on conservation laws for arbitrary differential equations is proved. The theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables. The new theorem does not require existence of a Lagrangian and is based on a concept of an adjoint equation for non-linear equations suggested recently by the author. It is proved that the adjoint equation inherits all symmetries of the original equation. Accordingly, one can associate a conservation law with any group of Lie, Lie-Backlund or non-local symmetries and find conservation laws for differential equations without classical Lagrangians.
Subfields: Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/f79e3878bafe915103095bb8281bb7f9fda3c992
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In Numerical Analysis
In Statistical and Nonlinear Physics
Citations in the corpus
- Nonlinear self-adjointness in constructing conservation laws (2011, background): “The Korteweg-de Vries (KdV) equation ut = uxxx + uux is strictly self-adjoint [3].”
- Conservation laws for time-fractional subdiffusion and diffusion-wave equations (2014, background): “It can be proved that in the limiting case of integer α these operators coincide with the known integer-order Noether operators presented in [26] (see also [22, 24, 27]).”
- Interaction solutions to Hirota-Satsuma-Ito equation in (2 + 1)-dimensions (2019, background): “, [32,45,48]), and yields the corresponding Lie-Bäcklund symmetries, which can be used to determine conservation laws by symmetries and adjoint symmetries [11,23,26].”
- Nonlinear self-adjointness and conservation laws (2011, methodology): “r equations was introduced [1] for constructing conservation laws associated with symmetries of differential equations. To extend the possibilities of the new method for constructing conservation laws [2] the notion of quasi self-adjointness was used in [3]. I suggest here the general concept of nonl”