Analogs of the Burgers equation of arbitrary order
Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 2, pp. 303-307
Voir la notice de l'article provenant de la source Math-Net.Ru
Nonlinear equations of the form
$$
\frac{\partial u}{\partial t}=\frac{\partial^n{u}}{\partial x^n}+F\biggl(x,u,\dots,\frac{\partial^{n-1}u}{\partial x^{n-1}}\biggr),\quad n\geqslant 2,
$$
are constructed; they are associated with linear substitutions of the Cole–Hopf type
and have an infinite set of local symmetries. For $n\leqslant 5$, these equations together
with equations of Korteweg–de Vries type exhaust the list of equations of the given
type possessing an infinite set of local symmetries.
@article{TMF_1985_65_2_a13,
author = {S. I. Svinolupov},
title = {Analogs of the {Burgers} equation of arbitrary order},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {303--307},
publisher = {mathdoc},
volume = {65},
number = {2},
year = {1985},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1985_65_2_a13/}
}
S. I. Svinolupov. Analogs of the Burgers equation of arbitrary order. Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 2, pp. 303-307. http://geodesic.mathdoc.fr/item/TMF_1985_65_2_a13/