Geodesic
Symmetries of scalar fields.~II
Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 3, pp. 382-391

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Local symmetries and conserved densities are calculated for a system of classical scalar fields in $(n+1)$-dimensional ($n>1$) space-time with Lagrangian of the form $$ L=\frac12h_{ab}(\varphi){\varphi_\nu}^a\varphi^{b\nu}-V(\varphi). $$ It is shown that, in contrast to two-dimensional theories, the existence of higher symmetries or conservation laws is possible only if in the field equations one can separate a linear subsystem by means of a point transformation $\varphi^a=f^a(\bar\varphi)$. In the case of an irreducible metric $h_{ab}$, all symmetries and conserved densities are found explicitly. An equation is obtained for the local conserved densities of an arbitrary generalized-evolution system. 
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     author = {A. G. Meshkov},
     title = {Symmetries of scalar {fields.~II}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {382--391},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_57_3_a5/}
}
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A. G. Meshkov. Symmetries of scalar fields.~II. Teoretičeskaâ i matematičeskaâ fizika, Tome 57 (1983) no. 3, pp. 382-391. http://geodesic.mathdoc.fr/item/TMF_1983_57_3_a5/