Integration of $D$-dimensional cosmological models with two factor spaces by reduction to the generalized Emden--Fowler equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 3, pp. 454-469
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The $D$-dimensional cosmological model on the manifold $M = R \times M_{1} \times \cdots\times M_{n}$, describing the evolution of Einstein factor spaces $M_i$ in the presence of a multicomponent perfect fluid source, is considered. The barotropic equation of state for the mass?energy densities and pressures of the components is assumed in each space. Where the number of non-Ricci-flat factor spaces and the number of perfect fluid components are both equal to two, the Einstein equations for the model are reduced to the generalized Emden–Fowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin using discrete-group analysis. We generate new integrable cosmological models using the integrable classes of this equation and present the corresponding metrics. The method is demonstrated for the special model with Ricci-flat spaces $M_1$ and $M_2$ and a two-component perfect fluid source
@article{TMF_1998_114_3_a9,
author = {V. R. Gavrilov and V. N. Melnikov},
title = {Integration of $D$-dimensional cosmological models with two factor spaces by reduction to the generalized {Emden--Fowler} equation},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {454--469},
publisher = {mathdoc},
volume = {114},
number = {3},
year = {1998},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1998_114_3_a9/}
}
TY - JOUR AU - V. R. Gavrilov AU - V. N. Melnikov TI - Integration of $D$-dimensional cosmological models with two factor spaces by reduction to the generalized Emden--Fowler equation JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1998 SP - 454 EP - 469 VL - 114 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1998_114_3_a9/ LA - ru ID - TMF_1998_114_3_a9 ER -
%0 Journal Article %A V. R. Gavrilov %A V. N. Melnikov %T Integration of $D$-dimensional cosmological models with two factor spaces by reduction to the generalized Emden--Fowler equation %J Teoretičeskaâ i matematičeskaâ fizika %D 1998 %P 454-469 %V 114 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1998_114_3_a9/ %G ru %F TMF_1998_114_3_a9
V. R. Gavrilov; V. N. Melnikov. Integration of $D$-dimensional cosmological models with two factor spaces by reduction to the generalized Emden--Fowler equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 114 (1998) no. 3, pp. 454-469. http://geodesic.mathdoc.fr/item/TMF_1998_114_3_a9/