Siberian Mathematical Journal

, Volume 47, Issue 4, pp 653–658 | Cite as

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

  • Yu. V. Zasorin


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.


Cauchy fundamental solution viscous transonic equation Kadomtsev-Petviashvili equation Kelvin-Voigt equation Korteweg-de Vries equation 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Yu. V. Zasorin
    • 1
  1. 1.Institute of Mathematics VoronezhVoronezh State UniversityRussia

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