Journal of Lie Theory

no. 2
On a Lie Group Characterization of Quasi-Local Symmetries of Nonlinear Evolution Equations
Journal of Lie Theory, Volume 20 (2010) no. 2, pp. 375-392
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.
DOI: 10.5802/jolt.601
Classification: 35Q80, 58Z05, 58J70
Keywords: Quasi-local symmetry, nonlinear evolution equation, Lie algebra 
@article{JOLT_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},
     year = {2010},
     volume = {20},
     number = {2},
     doi = {10.5802/jolt.601},
     zbl = {1197.35260},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.601/}
}
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R. Zhdanov. On a Lie Group Characterization of Quasi-Local Symmetries of Nonlinear Evolution Equations. Journal of Lie Theory, Volume 20 (2010) no. 2, pp. 375-392. doi: 10.5802/jolt.601

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