Geodesic
Equations invariant under differential substitutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 2, pp. 193-200 
V. S. Novikov. Equations invariant under differential substitutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 2, pp. 193-200. http://geodesic.mathdoc.fr/item/TMF_1998_116_2_a2/
@article{TMF_1998_116_2_a2,
     author = {V. S. Novikov},
     title = {Equations invariant under differential substitutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {193--200},
     year = {1998},
     volume = {116},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_116_2_a2/}
}
TY  - JOUR
AU  - V. S. Novikov
TI  - Equations invariant under differential substitutions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1998
SP  - 193
EP  - 200
VL  - 116
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1998_116_2_a2/
LA  - ru
ID  - TMF_1998_116_2_a2
ER  - 
%0 Journal Article
%A V. S. Novikov
%T Equations invariant under differential substitutions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1998
%P 193-200
%V 116
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1998_116_2_a2/
%G ru
%F TMF_1998_116_2_a2

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

The classification of differential autosubstitutions of the form $\hat u=G(u_x,u)$ that are allowed by general evolution equations with one spatial variable is considered. In the one-field case, every such substitution can be reduced to the autosubstitution $\hat u=u+u_x/u$ for the Burgers equation by a point transformation. This substitution is generalized to the two-field case.