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TMF, 1999, Volume 120, Number 1, Pages 3–19 (Mi tmf756)  

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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English version:
Theoretical and Mathematical Physics, 1999, 120:1, 821–833

Bibliographic databases:

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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\by V.~M.~Zhuravlev
\paper Exact solutions of the Liouville equation in multidimensional spaces
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\vol 120
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\pages 3--19
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 120
\issue 1
\pages 821--833
\crossref{https://doi.org/10.1007/BF02557392}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Zhuravlev, VM, “The scalar fields with negative kinetic energy, dark matter and dark energy”, General Relativity and Gravitation, 36:7 (2004), 1719  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. V. M. Zhuravlev, “Multidimensional nonlinear Klein–Gordon equations and rivertons”, Theoret. and Math. Phys., 197:3 (2018), 1701–1713  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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