Geodesic
Symmetries of scalar fields.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 2, pp. 197-204

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A definition of the generating operator of a system of nonlinear differential equations is proposed, and the connection between such operators and Lie–Bäcklund algebras is established. For classical nonlinear scalar fields in $n$-dimensional ($n>2$) space-time interacting through a potential the Lie–Bäcklund algebra is investigated, and it is concluded that there are no differential generating operators. It is shown that in nonlinear theory in $n$-dimensional ($n>2$) space-time the number of independent local conservation laws is always finite. 
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     author = {A. G. Meshkov},
     title = {Symmetries of scalar {fields.~I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {197--204},
     publisher = {mathdoc},
     volume = {55},
     number = {2},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_55_2_a3/}
}
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A. G. Meshkov. Symmetries of scalar fields.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 2, pp. 197-204. http://geodesic.mathdoc.fr/item/TMF_1983_55_2_a3/