Geodesic
Classes of generalized functional invariant solutions of wave equation.~I
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 418-435

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Proved that formula Smirnov–Sobolev give all real-valued functional invariant solutions of wave equation in space arbitrary dimension. Proved that solution with many phase functions are essential complex-valued. Considered problem finding of amplitude of generalized functional invariant solution for given phase.
Keywords: wave equation, generalized functional invariant solutions. 
@article{SEMR_2013_10_a51,
     author = {M. V. Neshchadim},
     title = {Classes of generalized functional invariant solutions of wave {equation.~I}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {418--435},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a51/}
}
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M. V. Neshchadim. Classes of generalized functional invariant solutions of wave equation.~I. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 418-435. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a51/