Geodesic
Exact solutions of the Liouville equation in multidimensional spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 1, pp. 3-19 Cet article a éte moissonné depuis la source Math-Net.Ru

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Exact solutions of the multidimensional Liouville equation, which are sought in the class of functional forms of the degree $n$ equal to the coordinate space dimension, are constructed based on a special representation of the Laplace and D'Alembert equations. The corresponding Liouville equation solutions are completely described in the coordinate space dimensions $d=3,4$. For $d>4$, the general solution form and the method for obtaining algebraic equations for the coefficients of functional $n$-forms is presented. 
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     author = {V. M. Zhuravlev},
     title = {Exact solutions of the {Liouville} equation in multidimensional spaces},
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V. M. Zhuravlev. Exact solutions of the Liouville equation in multidimensional spaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 120 (1999) no. 1, pp. 3-19. http://geodesic.mathdoc.fr/item/TMF_1999_120_1_a0/

[1] V. E. Zakharov, S. V. Manakov, S. P. Novikov, L. P. Pitaevskii, Teoriya solitonov: Metod obratnoi zadachi, Nauka, M., 1980 | MR

[2] R. Bullaf, F. Kodri (red.), Solitony, Mir, M., 1983

[3] R. Dodd, Dzh. Eilbek, Dzh. Gibbon, Kh. Morris, Solitony i nelineinye volnovye uravneniya, Mir, M., 1988 | MR

[4] A. N. Leznov, M. V. Savelev, Gruppovye metody integrirovaniya nelineinykh dinamicheskikh sistem, Nauka, M., 1985 | MR | Zbl

[5] V. M. Zhuravlev, ZhETF, 110:6 (1996), 2243 | MR

[6] V. M. Zhuravlev, Pisma v ZhETF, 65:3 (1997), 285

[7] V. M. Zhuravlev, ZhETF, 114:5 (1998), 1897 | MR

[8] V. M. Zhuravlev, PMM, 58:6 (1994), 61 | MR