Geodesic
Symmetries of differential ideals and differential equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 2, pp. 185-190

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The paper deals with differential rings and partial differential equations with coefficients in some algebra. We introduce symmetries and the conservation laws to the differential ideal of an arbitrary differential ring. We prove that a set of symmetries of an ideal forms a Lie ring and give a precise criterion when a differentiation is a symmetry of an ideal. These concepts are applied to partial differential equations.
Keywords: differential rings, symmetry, partial differential equations. 
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     author = {Oleg V. Kaptsov},
     title = {Symmetries of differential ideals and differential equations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {185--190},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_2_a4/}
}
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Oleg V. Kaptsov. Symmetries of differential ideals and differential equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 2, pp. 185-190. http://geodesic.mathdoc.fr/item/JSFU_2019_12_2_a4/