On reduction of some classes of partial differential equations to equations with fewer variables and exact solutions
- 20 Downloads
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.
KeywordsCauchy fundamental solution viscous transonic equation Kadomtsev-Petviashvili equation Kelvin-Voigt equation Korteweg-de Vries equation
Unable to display preview. Download preview PDF.
- 1.Demidenko G. V. and Uspenskii S. V., Equations and Systems That Are Not Solved with Respect to the Higher Derivative [in Russian], Nauchnaya Kniga, Novosibirsk (1998).Google Scholar
- 2.Dodd R.K., Eilbeck J. C., Gibbon J.D., and Morris H. C., Solitons and Nonlinear Wave Equations [Russian translation], Mir, Moscow (1988).Google Scholar
- 3.Bullough R. K. (ed.) and Caudrey P. J. (ed.), Solitons, Springer-Verlag, Berlin; Heidelberg; New York (1980).Google Scholar
- 5.Zasorin Yu. V. and Pridushchenko M. V., “Exact solutions of the spatial Kadomtsev-Petviashvili equation,” Vestnik VGU Ser. Fiz. Mat., No. 2, 133–136 (2002).Google Scholar
- 6.Hörmander L., Linear Partial Differential Operators [Russian translation], Mir, Moscow (1965).Google Scholar
- 7.Bateman H. and Erdélyi A., Higher Transcendental Functions. Bessel Functions, Parabolic Cylinder Functions, Orthogonal Polynomials [Russian translation], Nauka, Moscow (1974).Google Scholar
- 9.Schlichting H., Boundary-Layer Theory [Russian translation], Izdat. Inostr. Lit., Moscow (1956).Google Scholar
- 10.Olver F. W. J., Asymptotics and Special Functions [Russian translation], Nauka, Moscow (1990).Google Scholar