Geodesic
Ideals generated by differential equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 170-186

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

We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gröbner bases to clarify crucial notions concerning compatibility such as passivity and reducibility. One obtains sufficient conditions for a differential system to be passive and proves that such systems generate manifolds in the jet space. Some examples of constructions of passive systems associated with the sinh-Cordon equation are given.
Keywords: differential rings and ideals, Gröbner bases, partial differential equations. 
@article{JSFU_2020_13_2_a4,
     author = {Oleg V. Kaptsov},
     title = {Ideals generated by differential equations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {170--186},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a4/}
}
TY  - JOUR
AU  - Oleg V. Kaptsov
TI  - Ideals generated by differential equations
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2020
SP  - 170
EP  - 186
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a4/
LA  - en
ID  - JSFU_2020_13_2_a4
ER  - 
%0 Journal Article
%A Oleg V. Kaptsov
%T Ideals generated by differential equations
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2020
%P 170-186
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a4/
%G en
%F JSFU_2020_13_2_a4
Oleg V. Kaptsov. Ideals generated by differential equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 2, pp. 170-186. http://geodesic.mathdoc.fr/item/JSFU_2020_13_2_a4/