Title of article :
A new conservation theorem
Author/Authors :
Nail H. Ibragimov، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2007
Abstract :
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–Bäcklund or non-local symmetries and find conservation laws for differential
equations without classical Lagrangians.
© 2006 Published by Elsevier Inc.
Keywords :
Adjoint equation to non-linear equations , Symmetry of adjoint equations , Conservationtheorem , KdV equation , Lagrangian
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications