Geodesic
On a Lie Group Characterization of Quasi-Local Symmetries of Nonlinear Evolution Equations
Renat Zhdanov1
1BIO-key International, Eagan, MN 55123, U.S.A.
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

Renat Zhdanov  1

1 BIO-key International, Eagan, MN 55123, U.S.A. 
Renat 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/JOLT_2010_20_2_a7/
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     author = {Renat Zhdanov},
     title = {On a {Lie} {Group} {Characterization} of {Quasi-Local} {Symmetries} of {Nonlinear} {Evolution} {Equations}},
     journal = {Journal of Lie Theory},
     pages = {375--392},
     year = {2010},
     volume = {20},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2010_20_2_a7/}
}
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