Geodesic
On a Lie Group Characterization of Quasi-Local Symmetries of Nonlinear Evolution Equations
Journal of Lie theory, Tome 20 (2010) no. 2, pp. 375-392.

Voir la notice de l'article provenant de la source Heldermann Verlag

We develop an efficient algebraic approach to classifying nonlinear evolution equations in one spatial dimension that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. It applies to evolution equations invariant under Lie point symmetries leaving the temporal variable invariant. We construct inequivalent realizations of two- and three-dimensional Lie algebras leading to evolution equations admitting quasi-local symmetries. Finally, we generalize the approach in question for the case of an arbitrary system of evolution equations in two independent variables.
Classification : 35Q80, 58Z05, 58J70
Mots-clés : Quasi-local symmetry, nonlinear evolution equation, Lie algebra 
@article{JLT_2010_20_2_JLT_2010_20_2_a7,
     author = {R. Zhdanov },
     title = {On a {Lie} {Group} {Characterization} of {Quasi-Local} {Symmetries} of {Nonlinear} {Evolution} {Equations}},
     journal = {Journal of Lie theory},
     pages = {375--392},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JLT_2010_20_2_JLT_2010_20_2_a7/}
}
TY  - JOUR
AU  - R. Zhdanov 
TI  - On a Lie Group Characterization of Quasi-Local Symmetries of Nonlinear Evolution Equations
JO  - Journal of Lie theory
PY  - 2010
SP  - 375
EP  - 392
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JLT_2010_20_2_JLT_2010_20_2_a7/
ID  - JLT_2010_20_2_JLT_2010_20_2_a7
ER  - 
%0 Journal Article
%A R. Zhdanov 
%T On a Lie Group Characterization of Quasi-Local Symmetries of Nonlinear Evolution Equations
%J Journal of Lie theory
%D 2010
%P 375-392
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JLT_2010_20_2_JLT_2010_20_2_a7/
%F JLT_2010_20_2_JLT_2010_20_2_a7
R. Zhdanov . On a Lie Group Characterization of Quasi-Local Symmetries of Nonlinear Evolution Equations. Journal of Lie theory, Tome 20 (2010) no. 2, pp. 375-392. http://geodesic.mathdoc.fr/item/JLT_2010_20_2_JLT_2010_20_2_a7/