Geodesic
Exponentially localized solutions to the Klein--Gordon equation
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 30, Tome 275 (2001), pp. 187-198

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Explicit exponentially localized packet-like solutions to the Klein–Gordon equation are presented for the cases of two and three spacial variables. The appoach is based on complex ray theory. The nonlinear Klein–Gorgon equation is reduced to simple ordinary differential equation of complex solution of the eiconal equation. 
@article{ZNSL_2001_275_a13,
     author = {M. V. Perel' and I. V. Fialkovskii},
     title = {Exponentially localized solutions to the {Klein--Gordon} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {187--198},
     publisher = {mathdoc},
     volume = {275},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a13/}
}
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M. V. Perel'; I. V. Fialkovskii. Exponentially localized solutions to the Klein--Gordon equation. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 30, Tome 275 (2001), pp. 187-198. http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a13/