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On reduction of some classes of partial differential equations to equations with fewer variables and exact solutions

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Abstract

We establish a connection between the fundamental solutions to some classes of linear nonstationary partial differential equations and the fundamental solutions to other nonstationary equations with fewer variables. In particular, reduction enables us to obtain exact formulas for the fundamental solutions of some spatial nonstationary equations of mathematical physics (for example, the Kadomtsev-Petviashvili equation, the Kelvin-Voigt equation, etc.) from the available fundamental solutions to one-dimensional stationary equations.

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Authors and Affiliations

  1. Institute of Mathematics Voronezh, Voronezh State University, Russia

    Yu. V. Zasorin

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  1. Yu. V. Zasorin
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Original Russian Text Copyright © 2006 Zasorin Yu. V.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 4, pp. 791–797, July–August, 2006.

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Zasorin, Y.V. On reduction of some classes of partial differential equations to equations with fewer variables and exact solutions. Sib Math J 47, 653–658 (2006). https://doi.org/10.1007/s11202-006-0076-8

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  • DOI: https://doi.org/10.1007/s11202-006-0076-8

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