This article is cited in 1 paper

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

Yu. V. Zasorin

Voronezh State University

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.

Keywords: Cauchy fundamental solution, viscous transonic equation, Kadomtsev–Petviashvili equation, Kelvin–Voigt equation, Korteweg–de Vries equation.

UDC: 517.9

Received: 04.04.2005

 English version: Siberian Mathematical Journal, 2006, 47:4, 653–658

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