Geodesic
Essential Conservation Laws for Equations with Infinite Symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 190-198

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We consider partial differential equations of variational problems with infinite symmetry groups. We study local conservation laws associated with arbitrary functions of one variable in the group generators. We show that only symmetries with arbitrary functions of dependent variables lead to an infinite number of conservation laws. We also calculate local conservation laws for the potential Zabolotskaya–Khokhlov equation for one of its infinite subgroups.
Keywords: infinite symmetries, conservation laws. 
@article{TMF_2005_144_1_a19,
     author = {V. Rosenhaus},
     title = {Essential {Conservation} {Laws} for {Equations} with {Infinite} {Symmetries}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {190--198},
     publisher = {mathdoc},
     volume = {144},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a19/}
}
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V. Rosenhaus. Essential Conservation Laws for Equations with Infinite Symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 190-198. http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a19/