Geodesic
On multi-dimensional partial differential equations with power nonlinearities in first derivatives
Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 98-108

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{UFA_2017_9_1_a8,
     author = {I. V. Rakhmelevich},
     title = {On multi-dimensional partial differential equations with power nonlinearities in first derivatives},
     journal = {Ufa mathematical journal},
     pages = {98--108},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2017_9_1_a8/}
}
TY  - JOUR
AU  - I. V. Rakhmelevich
TI  - On multi-dimensional partial differential equations with power nonlinearities in first derivatives
JO  - Ufa mathematical journal
PY  - 2017
SP  - 98
EP  - 108
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UFA_2017_9_1_a8/
LA  - en
ID  - UFA_2017_9_1_a8
ER  - 
%0 Journal Article
%A I. V. Rakhmelevich
%T On multi-dimensional partial differential equations with power nonlinearities in first derivatives
%J Ufa mathematical journal
%D 2017
%P 98-108
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UFA_2017_9_1_a8/
%G en
%F UFA_2017_9_1_a8
I. V. Rakhmelevich. On multi-dimensional partial differential equations with power nonlinearities in first derivatives. Ufa mathematical journal, Tome 9 (2017) no. 1, pp. 98-108. http://geodesic.mathdoc.fr/item/UFA_2017_9_1_a8/