Geodesic
Analogs of the Burgers equation of arbitrary order
Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 2, pp. 303-307 
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/
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     title = {Analogs of the {Burgers} equation of arbitrary order},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1985_65_2_a13/}
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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.

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