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Exact solutions of the Liouville equation in multidimensional spaces

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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.

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Authors and Affiliations

  1. Ul'yanovsk State University, Ul'yanovsk, Russia

    V. M. Zhuravlev

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  1. V. M. Zhuravlev
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 1, pp. 3–19, July, 1999.

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Zhuravlev, V.M. Exact solutions of the Liouville equation in multidimensional spaces. Theor Math Phys 120, 821–833 (1999). https://doi.org/10.1007/BF02557392

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  • DOI: https://doi.org/10.1007/BF02557392

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