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This article is cited in 3 scientific papers (total in 3 papers)
Exact solutions of the Liouville equation in multidimensional spaces
V. M. Zhuravlev
Ulyanovsk State University
Abstract:
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.
DOI:
https://doi.org/10.4213/tmf756
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Theoretical and Mathematical Physics, 1999, 120:1, 821–833
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Received: 26.11.1998
Citation:
V. M. Zhuravlev, “Exact solutions of the Liouville equation in multidimensional spaces”, TMF, 120:1 (1999), 3–19; Theoret. and Math. Phys., 120:1 (1999), 821–833
Citation in format AMSBIB
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\pages 821--833
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http://mi.mathnet.ru/eng/tmf756https://doi.org/10.4213/tmf756 http://mi.mathnet.ru/eng/tmf/v120/i1/p3
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This publication is cited in the following articles:
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V. M. Zhuravlev, “Exact solutions of the nonlinear diffusion equation $u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space”, Theoret. and Math. Phys., 124:2 (2000), 1082–1093
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Zhuravlev, VM, “The scalar fields with negative kinetic energy, dark matter and dark energy”, General Relativity and Gravitation, 36:7 (2004), 1719
  -
V. M. Zhuravlev, “Multidimensional nonlinear Klein–Gordon equations and rivertons”, Theoret. and Math. Phys., 197:3 (2018), 1701–1713
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