In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries.
Gubbiotti, G., Levi, D., Scimiterna, C. (2016). On partial differential and difference equations with symmetries depending on arbitrary functions. ACTA POLYTECHNICA, 56(3), 193-201 [10.14311/AP.2016.56.0193].
On partial differential and difference equations with symmetries depending on arbitrary functions
GUBBIOTTI, GIORGIO;LEVI, Decio;SCIMITERNA, CHRISTIAN
2016-01-01
Abstract
In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries.File in questo prodotto:
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