Abstract:
We consider a class of multi-dimensional partial differential equations involving a linear differential operator of arbitrary order and a power nonlinearity in the first derivatives. Under some additional assumptions for this operator, we study the solutions of multi-dimensional travelling waves that depend on some linear combinations of the original variables. The original equation is transformed to a reduced one, which can be solved by the separation of variables. Solutions of the reduced equation are found for the cases of additive, multiplicative and combined separation of variables.
Keywords:
partial differential equation, reduced equation, method of separation of variables, power nonlinearity.
Citation:
I. V. Rakhmelevich, “On multi-dimensional partial differential equations with power nonlinearities in first derivatives”, Ufa Math. J., 9:1 (2017), 98–108
\Bibitem{Rak17}
\by I.~V.~Rakhmelevich
\paper On multi-dimensional partial differential equations with power nonlinearities in first derivatives
\jour Ufa Math. J.
\yr 2017
\vol 9
\issue 1
\pages 98--108
\mathnet{http://mi.mathnet.ru/eng/ufa369}
\crossref{https://doi.org/10.13108/2017-9-1-98}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000411736500009}
\elib{https://elibrary.ru/item.asp?id=29009899}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85018772484}
Linking options:
https://www.mathnet.ru/eng/ufa369
https://doi.org/10.13108/2017-9-1-98
https://www.mathnet.ru/eng/ufa/v9/i1/p98
This publication is cited in the following 6 articles:
Chetan Rathod, “PAPER ON ANALYTICAL SOLUTION OF HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS”, ShodhKosh J. Vis. Per. Arts, 2:2 (2022)
I. V. Rakhmelevich, “O multiplikativnykh mnogomernykh differentsialnykh uravneniyakh v chastnykh proizvodnykh”, Vladikavk. matem. zhurn., 23:1 (2021), 43–59
I. V. Rakhmelevich, “Modified Bianchi equation with nonlinear right-hand side”, Russian Math. (Iz. VUZ), 65:10 (2021), 44–51
L. L. Ryskina, “Nakhozhdenie osobykh reshenii mnogomernykh differentsialnykh uravnenii tipa Klero v chastnykh proizvodnykh s trigonometricheskimi funktsiyami”, Kompyuternye issledovaniya i modelirovanie, 12:1 (2020), 33–42
I. V. Rakhmelevich, “O mnogomernykh determinantnykh differentsialno-operatornykh
uravneniyakh”, Vladikavk. matem. zhurn., 22:2 (2020), 53–69
I. V. Rakhmelevich, “Dvumernoe neavtonomnoe giperbolicheskoe uravnenie vtorogo poryadka so stepennymi nelineinostyami”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2017, no. 49, 52–60
Citation in format AMSBIB
Contact us: