Geodesic
Regular solutions of the Liouville equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 1, pp. 33-39 
G. P. Jorjadze. Regular solutions of the Liouville equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 41 (1979) no. 1, pp. 33-39. http://geodesic.mathdoc.fr/item/TMF_1979_41_1_a4/
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     author = {G. P. Jorjadze},
     title = {Regular solutions of the {Liouville} equation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the Liouville equation $\varphi_{tt}(t,x)-\varphi_{xx}(t,x)\pm(m^2/2)e^{\varphi(t,x)}=0$ the Goursat problem is solved explicitly and the properties of regular solutions are investigated. The Liouville equation is regarded as a model of a self-interacting scalar field. The asymptotic fields, the classical $S$ matrix, and observable quantities such as the energy and momentum are constructed.

[1] J. Liouvill, J. Math. Pures Appl., 18 (1853), 71

[2] G. P. Dzhordzhadze, A. K. Pogrebkov, M. K. Polivanov, DAN SSSR, 243 (1978), 318 | MR | Zbl

[3] A. K. Pogrebkov, DAN SSSR, 244 (1979), 873 | MR | Zbl

[4] V. A. Andreev, TMF, 29 (1976), 2

[5] G. P. Jorjadze, A. K. Pogrebkov, M. K. Polivanov, Preprint IC/78/126, Trieste, 1978 | MR